Презентация "Синус, косинус и тангенс острого угла прямоугольного треугольника"

Геометрия.

«Соотношения между сторонами и углами прямоугольного треугольника»

катет

Гипотенуза

В

с

а

катет

А

С

b

Гипотенуза –наибольшая сторона ,

а катеты –стороны,

проведенные под прямым углом.

Расположение углов и сторон

А

АС – противолежащий катет

c

b

С

В

a

ВС – прилежащий катет

Расположение углов и сторон

А

ВС - противолежащий катет

c

b

С

В

a

АС – прилежащий катет

К

Назвать катет, прилежащий к углу К.

Назвать катет, прилежащий к углу Т.

Назвать катет, противолежащий углу К.

Назвать катет, противолежащий углу Т.

Р

Т

• Острый угол прямоугольного треугольника зависит от гипотенузы, от катетов.

Примечание:

« Зная длины сторон прямоугольного треугольника можно вычислить его острый угол. Но для этого надо знать тригонометрические функции: «синус», «косинус»,»тангенс», «котангенс» .

Синусом острого угла прямоугольного треугольника называется отношение противолежащего катета к гипотенузе.

A

C

B

Косинусом острого угла прямоугольного треугольника называется отношение прилежащего катета к гипотенузе.

A

C

B

Тангенсом острого угла прямоугольного треугольника называется отношение противолежащего катета к прилежащему катету.

A

C

B

Тангенс угла равен отношению синуса к косинусу этого угла.

B

C

A

Практическая пятиминутка

• Дан прямоугольный треугольник АВС с острым углом А. Известно, что сторона ВС = 2/3, а АС = 1/3.
• Найдите: tg A = ? ctg A = ?

В

с

а

А

С

b

Найти: 1) sin  A,

4) сtg  A,

2) cоs  A,

3) tg  A,

Ответ:

sin  A=

Ответ:

соs  A=

В

tg  A=

сtg  A=

13 см

5см

С

А

РАБОТА НА УРОКЕ

№ 591, 592

Найдите синус, косинус, тангенс и котангенс углов A и B треугольника ABC с прямым углом C , если

а) BC = 21 A С = 20

б) BC = 1 AC = 2

в) AC = 24 AB = 25

(а), в) – вместе, б) – сами)

A

C

B

а) cos α = a b size 12{"cos" α = { {a} over {b} } } {} AQAJAAADUAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA0AGEgAAACYGDwAaAP////8AABAAAADA////tv///wAG AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgAC+AQFAAAAEwIAAusFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdqQPZuQEAAAALQEBAAgAAAAyCosDDgUBAAAAYnkIAAAAMgpwARIF AQAAAGF5HAAAAPsCgP4AAAAAAACQAQAAAAIEAgAQU3ltYm9sAHbWDQobmAUtABTxEgB5SFB2 QJFTdqQPZuQEAAAALQECAAQAAADwAQEACAAAADIKYALJAwEAAAA9eRwAAAD7AoD+AAAAAAAA kAEAAAAABAIAEFRpbWVzIE5ldyBSb21hbgAU8RIAeUhQdkCRU3akD2bkBAAAAC0BAQAEAAAA 8AECAAgAAAAyCmACbwMBAAAAIHkIAAAAMgpgAiUCAQAAACB5CQAAADIKYAI0AAMAAABjb3Nl HAAAAPsCgP4AAAAAAACQAQEAAAIEAgAQU3ltYm9sAHbWDQocmAUtABTxEgB5SFB2QJFTdqQP ZuQEAAAALQECAAQAAADwAQEACAAAADIKYAJhAgEAAABhbwoAAAAmBg8ACgD/////AQAAAAAA HAAAAPsCEAAHAAAAAAC8AgAAAMwBAgIiU3lzdGVtAOSkD2bkAAAKADgAigEAAAAAAQAAADDz EgAEAAAALQEBAAQAAADwAQIAAwAAAAAA ; б) cos α = a c size 12{"cos" α = { {a} over {c} } } {} AQAJAAADUAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA0AGEgAAACYGDwAaAP////8AABAAAADA////tv///wAG AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgAC+AQFAAAAEwIAAusFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdu4RZjcEAAAALQEBAAgAAAAyCosDGgUBAAAAY3kIAAAAMgpwARIF AQAAAGF5HAAAAPsCgP4AAAAAAACQAQAAAAIEAgAQU3ltYm9sAHYqEAo/2AUtABTxEgB5SFB2 QJFTdu4RZjcEAAAALQECAAQAAADwAQEACAAAADIKYALJAwEAAAA9eRwAAAD7AoD+AAAAAAAA kAEAAAAABAIAEFRpbWVzIE5ldyBSb21hbgAU8RIAeUhQdkCRU3buEWY3BAAAAC0BAQAEAAAA 8AECAAgAAAAyCmACbwMBAAAAIHkIAAAAMgpgAiUCAQAAACB5CQAAADIKYAI0AAMAAABjb3Nl HAAAAPsCgP4AAAAAAACQAQEAAAIEAgAQU3ltYm9sAHYqEApA2AUtABTxEgB5SFB2QJFTdu4R ZjcEAAAALQECAAQAAADwAQEACAAAADIKYAJhAgEAAABhbwoAAAAmBg8ACgD/////AQAAAAAA HAAAAPsCEAAHAAAAAAC8AgAAAMwBAgIiU3lzdGVtADfuEWY3AAAKADgAigEAAAAAAQAAADDz EgAEAAAALQEBAAQAAADwAQIAAwAAAAAA ;

в) cos α = b c size 12{"cos" α = { {b} over {c} } } {} AQAJAAADUAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgAyAGEgAAACYGDwAaAP////8AABAAAADA////tv///+AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgAC+AQFAAAAEwIAAtoFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdgURZhgEAAAALQEBAAgAAAAyCosDEgUBAAAAY3kIAAAAMgpwAQYF AQAAAGJ5HAAAAPsCgP4AAAAAAACQAQAAAAIEAgAQU3ltYm9sAHYeEgoFGAYtABTxEgB5SFB2 QJFTdgURZhgEAAAALQECAAQAAADwAQEACAAAADIKYALJAwEAAAA9eRwAAAD7AoD+AAAAAAAA kAEAAAAABAIAEFRpbWVzIE5ldyBSb21hbgAU8RIAeUhQdkCRU3YFEWYYBAAAAC0BAQAEAAAA 8AECAAgAAAAyCmACbwMBAAAAIHkIAAAAMgpgAiUCAQAAACB5CQAAADIKYAI0AAMAAABjb3Nl HAAAAPsCgP4AAAAAAACQAQEAAAIEAgAQU3ltYm9sAHYeEgoGGAYtABTxEgB5SFB2QJFTdgUR ZhgEAAAALQECAAQAAADwAQEACAAAADIKYAJhAgEAAABhbwoAAAAmBg8ACgD/////AQAAAAAA HAAAAPsCEAAHAAAAAAC8AgAAAMwBAgIiU3lzdGVtABgFEWYYAAAKADgAigEAAAAAAQAAADDz EgAEAAAALQEBAAQAAADwAQIAAwAAAAAA ; г) cos α = b a size 12{"cos" α = { {b} over {a} } } {} AQAJAAADUAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA0AGEgAAACYGDwAaAP////8AABAAAADA////tv///wAG AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgAC+AQFAAAAEwIAAusFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdgQSZk8EAAAALQEBAAgAAAAyCosDEgUBAAAAYXkIAAAAMgpwAQ4F AQAAAGJ5HAAAAPsCgP4AAAAAAACQAQAAAAIEAgAQU3ltYm9sAHYMEAqleAUtABTxEgB5SFB2 QJFTdgQSZk8EAAAALQECAAQAAADwAQEACAAAADIKYALJAwEAAAA9eRwAAAD7AoD+AAAAAAAA kAEAAAAABAIAEFRpbWVzIE5ldyBSb21hbgAU8RIAeUhQdkCRU3YEEmZPBAAAAC0BAQAEAAAA 8AECAAgAAAAyCmACbwMBAAAAIHkIAAAAMgpgAiUCAQAAACB5CQAAADIKYAI0AAMAAABjb3Nl HAAAAPsCgP4AAAAAAACQAQEAAAIEAgAQU3ltYm9sAHYMEAqmeAUtABTxEgB5SFB2QJFTdgQS Zk8EAAAALQECAAQAAADwAQEACAAAADIKYAJhAgEAAABhbwoAAAAmBg8ACgD/////AQAAAAAA HAAAAPsCEAAHAAAAAAC8AgAAAMwBAgIiU3lzdGVtAE8EEmZPAAAKADgAigEAAAAAAQAAADDz EgAEAAAALQEBAAQAAADwAQIAAwAAAAAA .

а) tg β = a b size 12{ ital "tg" β = { {a} over {b} } } {} AQAJAAADTwEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA4AFEgAAACYGDwAaAP////8AABAAAADA////tv///0AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACRAQFAAAAEwIAAjgFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdpwSZscEAAAALQEBAAgAAAAyCosDXAQBAAAAYnkIAAAAMgpwAV4E AQAAAGF5CAAAADIKYAIuAAIAAAB0ZxwAAAD7AoD+AAAAAAAAkAEAAAACBAIAEFN5bWJvbAB2 TBAKD1gGLQAU8RIAeUhQdkCRU3acEmbHBAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACFgMBAAAA PWccAAAA+wKA/gAAAAAAAJABAAAAAAQCABBUaW1lcyBOZXcgUm9tYW4AFPESAHlIUHZAkVN2 nBJmxwQAAAAtAQEABAAAAPABAgAIAAAAMgpgArwCAQAAACBnCAAAADIKYAJmAQEAAAAgZxwA AAD7AoD+AAAAAAAAkAEBAAACBAIAEFN5bWJvbAB2TBAKEFgGLQAU8RIAeUhQdkCRU3acEmbH BAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACxgEBAAAAYmcKAAAAJgYPAAoA/////wEAAAAAABwA AAD7AhAABwAAAAAAvAIAAADMAQICIlN5c3RlbQDHnBJmxwAACgA4AIoBAAAAAAEAAAAw8xIA BAAAAC0BAQAEAAAA8AECAAMAAAAAAA== ; б) tg β = b c size 12{ ital "tg" β = { {b} over {c} } } {} AQAJAAADTwEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA4AFEgAAACYGDwAaAP////8AABAAAADA////tv///0AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACRQQFAAAAEwIAAicFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdrkNZtMEAAAALQEBAAgAAAAyCosDXwQBAAAAY3kIAAAAMgpwAVME AQAAAGJ5CAAAADIKYAIuAAIAAAB0ZxwAAAD7AoD+AAAAAAAAkAEAAAACBAIAEFN5bWJvbAB2 cxIKmxgGLQAU8RIAeUhQdkCRU3a5DWbTBAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACFgMBAAAA PWccAAAA+wKA/gAAAAAAAJABAAAAAAQCABBUaW1lcyBOZXcgUm9tYW4AFPESAHlIUHZAkVN2 uQ1m0wQAAAAtAQEABAAAAPABAgAIAAAAMgpgArwCAQAAACBnCAAAADIKYAJmAQEAAAAgZxwA AAD7AoD+AAAAAAAAkAEBAAACBAIAEFN5bWJvbAB2cxIKnBgGLQAU8RIAeUhQdkCRU3a5DWbT BAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACxgEBAAAAYmcKAAAAJgYPAAoA/////wEAAAAAABwA AAD7AhAABwAAAAAAvAIAAADMAQICIlN5c3RlbQDTuQ1m0wAACgA4AIoBAAAAAAEAAAAw8xIA BAAAAC0BAQAEAAAA8AECAAMAAAAAAA== ; в) tg β = a c size 12{ ital "tg" β = { {a} over {c} } } {} AQAJAAADTwEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA4AFEgAAACYGDwAaAP////8AABAAAADA////tv///0AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACRAQFAAAAEwIAAjgFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdn0SZiwEAAAALQEBAAgAAAAyCosDZwQBAAAAY3kIAAAAMgpwAV4E AQAAAGF5CAAAADIKYAIuAAIAAAB0ZxwAAAD7AoD+AAAAAAAAkAEAAAACBAIAEFN5bWJvbAB2 qhEKktgFLQAU8RIAeUhQdkCRU3Z9EmYsBAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACFgMBAAAA PWccAAAA+wKA/gAAAAAAAJABAAAAAAQCABBUaW1lcyBOZXcgUm9tYW4AFPESAHlIUHZAkVN2 fRJmLAQAAAAtAQEABAAAAPABAgAIAAAAMgpgArwCAQAAACBnCAAAADIKYAJmAQEAAAAgZxwA AAD7AoD+AAAAAAAAkAEBAAACBAIAEFN5bWJvbAB2qhEKk9gFLQAU8RIAeUhQdkCRU3Z9EmYs BAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACxgEBAAAAYmcKAAAAJgYPAAoA/////wEAAAAAABwA AAD7AhAABwAAAAAAvAIAAADMAQICIlN5c3RlbQAsfRJmLAAACgA4AIoBAAAAAAEAAAAw8xIA BAAAAC0BAQAEAAAA8AECAAMAAAAAAA== ; г) tg β = b a size 12{ ital "tg" β = { {b} over {a} } } {} AQAJAAADTwEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgA4AFEgAAACYGDwAaAP////8AABAAAADA////tv///0AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACRAQFAAAAEwIAAjgFHAAAAPsCgP4AAAAAAACQAQEAAAAEAgAQVGltZXMgTmV3IFJv bWFuAPzfEgB5SFB2QJFTdkwQZrcEAAAALQEBAAgAAAAyCosDXgQBAAAAYXkIAAAAMgpwAVwE AQAAAGJ5CAAAADIKYAIuAAIAAAB0ZxwAAAD7AoD+AAAAAAAAkAEAAAACBAIAEFN5bWJvbAB2 rg8K2HgFLQD83xIAeUhQdkCRU3ZMEGa3BAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACFgMBAAAA PWccAAAA+wKA/gAAAAAAAJABAAAAAAQCABBUaW1lcyBOZXcgUm9tYW4A/N8SAHlIUHZAkVN2 TBBmtwQAAAAtAQEABAAAAPABAgAIAAAAMgpgArwCAQAAACBnCAAAADIKYAJmAQEAAAAgZxwA AAD7AoD+AAAAAAAAkAEBAAACBAIAEFN5bWJvbAB2rg8K2XgFLQD83xIAeUhQdkCRU3ZMEGa3 BAAAAC0BAgAEAAAA8AEBAAgAAAAyCmACxgEBAAAAYmcKAAAAJgYPAAoA/////wEAAAAAABwA AAD7AhAABwAAAAAAvAIAAADMAQICIlN5c3RlbQC3TBBmtwAACgA4AIoBAAAAAAEAAAAY4hIA BAAAAC0BAQAEAAAA8AECAAMAAAAAAA== .

• Для треугольника АВС , где АВ=7 , справедливо равенство:

а) sin A = 4 5 size 12{"sin" A = { {4} over {5} } } {} AQAJAAADLAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgAwAGEgAAACYGDwAaAP////8AABAAAADA////tv///8AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACwgQFAAAAEwIAAqkFHAAAAPsCgP4AAAAAAACQAQAAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTducSZlwEAAAALQEBAAgAAAAyCosD2AQBAAAANXkIAAAAMgpwAdwE AQAAADR5CAAAADIKYAI6AwEAAAAgeQgAAAAyCmAC8AEBAAAAIHkJAAAAMgpgAi4AAwAAAHNp bmUcAAAA+wKA/gAAAAAAAJABAAAAAgQCABBTeW1ib2wAdo8QCjiYBi0AFPESAHlIUHZAkVN2 5xJmXAQAAAAtAQIABAAAAPABAQAIAAAAMgpgApQDAQAAAD1pHAAAAPsCgP4AAAAAAACQAQEA AAAEAgAQVGltZXMgTmV3IFJvbWFuABTxEgB5SFB2QJFTducSZlwEAAAALQEBAAQAAADwAQIA CAAAADIKYAJoAgEAAABBaQoAAAAmBg8ACgD/////AQAAAAAAHAAAAPsCEAAHAAAAAAC8AgAA AMwBAgIiU3lzdGVtAFznEmZcAAAKADgAigEAAAAAAgAAADDzEgAEAAAALQECAAQAAADwAQEA AwAAAAAA ; б) sin A = 5 7 size 12{"sin" A = { {5} over {7} } } {} AQAJAAADLAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgAwAGEgAAACYGDwAaAP////8AABAAAADA////tv///8AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACwgQFAAAAEwIAAqkFHAAAAPsCgP4AAAAAAACQAQAAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdicSZnQEAAAALQEBAAgAAAAyCosD1gQBAAAAN3kIAAAAMgpwAdgE AQAAADV5CAAAADIKYAI6AwEAAAAgeQgAAAAyCmAC8AEBAAAAIHkJAAAAMgpgAi4AAwAAAHNp bmUcAAAA+wKA/gAAAAAAAJABAAAAAgQCABBTeW1ib2wAdjoRCsmYBi0AFPESAHlIUHZAkVN2 JxJmdAQAAAAtAQIABAAAAPABAQAIAAAAMgpgApQDAQAAAD1pHAAAAPsCgP4AAAAAAACQAQEA AAAEAgAQVGltZXMgTmV3IFJvbWFuABTxEgB5SFB2QJFTdicSZnQEAAAALQEBAAQAAADwAQIA CAAAADIKYAJoAgEAAABBaQoAAAAmBg8ACgD/////AQAAAAAAHAAAAPsCEAAHAAAAAAC8AgAA AMwBAgIiU3lzdGVtAHQnEmZ0AAAKADgAigEAAAAAAgAAADDzEgAEAAAALQECAAQAAADwAQEA AwAAAAAA ; в) sin A = 4 7 size 12{"sin" A = { {4} over {7} } } {} AQAJAAADLAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgAwAGEgAAACYGDwAaAP////8AABAAAADA////tv///8AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACwgQFAAAAEwIAAqkFHAAAAPsCgP4AAAAAAACQAQAAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdqQPZpAEAAAALQEBAAgAAAAyCosD1gQBAAAAN3kIAAAAMgpwAdwE AQAAADR5CAAAADIKYAI6AwEAAAAgeQgAAAAyCmAC8AEBAAAAIHkJAAAAMgpgAi4AAwAAAHNp bmUcAAAA+wKA/gAAAAAAAJABAAAAAgQCABBTeW1ib2wAdkYSCi6YBi0AFPESAHlIUHZAkVN2 pA9mkAQAAAAtAQIABAAAAPABAQAIAAAAMgpgApQDAQAAAD1pHAAAAPsCgP4AAAAAAACQAQEA AAAEAgAQVGltZXMgTmV3IFJvbWFuABTxEgB5SFB2QJFTdqQPZpAEAAAALQEBAAQAAADwAQIA CAAAADIKYAJoAgEAAABBaQoAAAAmBg8ACgD/////AQAAAAAAHAAAAPsCEAAHAAAAAAC8AgAA AMwBAgIiU3lzdGVtAJCkD2aQAAAKADgAigEAAAAAAgAAADDzEgAEAAAALQECAAQAAADwAQEA AwAAAAAA ; г) sin A = 7 5 size 12{"sin" A = { {7} over {5} } } {} AQAJAAADLAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgAwAGEgAAACYGDwAaAP////8AABAAAADA////tv///8AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgACwgQFAAAAEwIAAqkFHAAAAPsCgP4AAAAAAACQAQAAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdiMTZkQEAAAALQEBAAgAAAAyCosD2AQBAAAANXkIAAAAMgpwAdYE AQAAADd5CAAAADIKYAI6AwEAAAAgeQgAAAAyCmAC8AEBAAAAIHkJAAAAMgpgAi4AAwAAAHNp bmUcAAAA+wKA/gAAAAAAAJABAAAAAgQCABBTeW1ib2wAdk0PCn1YBi0AFPESAHlIUHZAkVN2 IxNmRAQAAAAtAQIABAAAAPABAQAIAAAAMgpgApQDAQAAAD1pHAAAAPsCgP4AAAAAAACQAQEA AAAEAgAQVGltZXMgTmV3IFJvbWFuABTxEgB5SFB2QJFTdiMTZkQEAAAALQEBAAQAAADwAQIA CAAAADIKYAJoAgEAAABBaQoAAAAmBg8ACgD/////AQAAAAAAHAAAAPsCEAAHAAAAAAC8AgAA AMwBAgIiU3lzdGVtAEQjE2ZEAAAKADgAigEAAAAAAgAAADDzEgAEAAAALQECAAQAAADwAQEA AwAAAAAA .

• Для треугольника АВС , где АВ=7 , справедливо равенство:

а) ctg A = 3 8 size 12{ ital "ctg"" A "= { {3} over {8} } } {} AQAJAAADLAEAAAMAHAAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADALgAyAGEgAAACYGDwAaAP////8AABAAAADA////tv///+AF AACWAwAACwAAACYGDwAMAE1hdGhUeXBlAADAAAgAAAD6AgAAEAAAAAAAAAAEAAAALQEAAAUA AAAUAgAC/AQFAAAAEwIAAswFHAAAAPsCgP4AAAAAAACQAQAAAAAEAgAQVGltZXMgTmV3IFJv bWFuABTxEgB5SFB2QJFTdpASZkMEAAAALQEBAAgAAAAyCosDBAUBAAAAOHkIAAAAMgpwAQoF AQAAADN5CAAAADIKYAKcBAEAAAAgeQgAAAAyCmACbgICAAAAQSAIAAAAMgpgAhQCAQAAACAg HAAAAPsCgP4AAAAAAACQAQAAAAIEAgAQU3ltYm9sAHaaDwqCIDcuABTxEgB5SFB2QJFTdpAS ZkMEAAAALQECAAQAAADwAQEACAAAADIKYALWAwEAAAA9IBwAAAD7AoD+AAAAAAAAkAEBAAAA BAIAEFRpbWVzIE5ldyBSb21hbgAU8RIAeUhQdkCRU3aQEmZDBAAAAC0BAQAEAAAA8AECAAkA AAAyCmACNAADAAAAY3RnZQoAAAAmBg8ACgD/////AQAAAAAAHAAAAPsCEAAHAAAAAAC8AgAA AMwBAgIiU3lzdGVtAEOQEmZDAAAKADgAigEAAAAAAgAAADDzEgAEAAAALQECAAQAAADwAQEA AwAAAAAA ; б) {} AQAJAAADUQAAAAAAEgAAAAAABQAAAAkCAAAAAAUAAAACAQEAAAAFAAAAAQL///8ABQAAAC4B GAAAAAUAAAALAgAAAAAFAAAADAIgAiABEgAAACYGDwAaAP////8AABAAAADA////pv///+AA AADGAQAACwAAACYGDwAMAE1hdGhUeXBlAABQAAoAAAAmBg8ACgD/////AQAAAAAAAwAAAAAA ctg A = 5 3 size 12{ ital "ctg"" A "= { {5} over {3} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAZcHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAJYHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQSDV AQAAAAD//wMAIABBACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAD/BQAAcgEAAAEANdMAAAAAAP// AQA1AIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA5AUA ANwBAADnBgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAP8FAACEAwAAAQAz0wAA AAAA//8BADMAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; в) ctg A = 5 8 size 12{ ital "ctg"" A "= { {5} over {8} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAZsHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAJoHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQSDV AQAAAAD//wMAIABBACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAD/BQAAcgEAAAEANdMAAAAAAP// AQA1AIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA5AUA ANwBAADrBgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAP8FAACEAwAAAQA40wAA AAAA//8BADgAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; г) ctg A = 3 5 size 12{ ital "ctg"" A "= { {3} over {5} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAZcHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAJYHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQSDV AQAAAAD//wMAIABBACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAD/BQAAcgEAAAEAM9MAAAAAAP// AQAzAIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA5AUA ANwBAADnBgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAP8FAACEAwAAAQA10wAA AAAA//8BADUAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA=

а) tg β = a b size 12{ ital "tg" β = { {a} over {b} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQwGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAAsGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAYQIAAAIAdGdIAQAA AAD//wIAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9u IFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIA AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAPcBAABhAgAAAgDOstIAAAAA AP//AQCyA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAA AAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAF AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAOUCAABhAgAAAQAAAD0ATwEAAAAA//8BAD0A jAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAA AACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwABAAUA AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAcgQAAHIBAAABAGHTAAAAAAD//wEAYQCMAAEA AAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2AAAA CgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAA iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAAFcEAADcAQAAYQUA APABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJp ZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAByBAAAhAMAAAEAYtMAAAAAAP//AQBi AIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA ; б) tg β = a c size 12{ ital "tg" β = { {a} over {c} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQwGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAAsGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAYQIAAAIAdGdIAQAA AAD//wIAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9u IFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIA AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAPcBAABhAgAAAgDOstIAAAAA AP//AQCyA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAA AAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAF AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAOUCAABhAgAAAQAAAD0ATwEAAAAA//8BAD0A jAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAA AACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwABAAUA AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAcgQAAHIBAAABAGHTAAAAAAD//wEAYQCMAAEA AAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2AAAA CgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAA iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAAFcEAADcAQAAYQUA APABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJp ZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACMBAAAhAMAAAEAY7sAAAAAAP//AQBj AIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA ;

в) tg β = b c size 12{ ital "tg" β = { {b} over {c} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQwGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAAsGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAYQIAAAIAdGdIAQAA AAD//wIAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9u IFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIA AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAPcBAABhAgAAAgDOstIAAAAA AP//AQCyA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAA AAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAF AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAOUCAABhAgAAAQAAAD0ATwEAAAAA//8BAD0A jAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAA AACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwABAAUA AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAcgQAAHIBAAABAGLTAAAAAAD//wEAYgCMAAEA AAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2AAAA CgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAA iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAAFcEAADcAQAAYQUA APABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJp ZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAACMBAAAhAMAAAEAY7sAAAAAAP//AQBj AIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA ; г) tg β = b a size 12{ ital "tg" β = { {b} over {a} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQwGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAAsGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABoAAABqAAAAYQIAAAIAdGdIAQAA AAD//wIAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9u IFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIA AAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAPcBAABhAgAAAgDOstIAAAAA AP//AQCyA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9sAAAA AAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcAAQAF AAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAOUCAABhAgAAAQAAAD0ATwEAAAAA//8BAD0A jAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYAAAAA AACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwABAAUA AAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAcgQAAHIBAAABAGLTAAAAAAD//wEAYgCMAAEA AAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2AAAA CgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAA iAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAAFcEAADcAQAAYQUA APABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJp ZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCH AAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAByBAAAhAMAAAEAYdMAAAAAAP//AQBh AIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA .

а) sin α = a b size 12{"sin" α = { {a} over {b} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbYGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALUGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAc2lu7AEA AAAA//8DAHMAaQBuAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAJUCAABhAgAAAgDOsd0A AAAAAP//AQCxA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9s AAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAJ4DAABhAgAAAQAAAD0ATwEAAAAA//8B AD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYA AAAAAACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKwUAAHIBAAABAGHTAAAAAAD//wEAYQCM AAEAAAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2 AAAACgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAA AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAABAFAADcAQAA GgYAAPABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAArBQAAhAMAAAEAYtMAAAAAAP// AQBiAIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA ; б) sin α = b c size 12{"sin" α = { {b} over {c} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbYGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALUGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAc2lu7AEA AAAA//8DAHMAaQBuAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAJUCAABhAgAAAgDOsd0A AAAAAP//AQCxA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9s AAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAJ4DAABhAgAAAQAAAD0ATwEAAAAA//8B AD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYA AAAAAACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKwUAAHIBAAABAGLTAAAAAAD//wEAYgCM AAEAAAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2 AAAACgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAA AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAABAFAADcAQAA GgYAAPABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAArBQAAhAMAAAEAY7sAAAAAAP// AQBjAIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA ; в) sin α = a c size 12{"sin" α = { {a} over {c} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbYGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALUGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAc2lu7AEA AAAA//8DAHMAaQBuAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAJUCAABhAgAAAgDOsd0A AAAAAP//AQCxA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9s AAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAJ4DAABhAgAAAQAAAD0ATwEAAAAA//8B AD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYA AAAAAACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKwUAAHIBAAABAGHTAAAAAAD//wEAYQCM AAEAAAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2 AAAACgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAA AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAABAFAADcAQAA GgYAAPABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAArBQAAhAMAAAEAY7sAAAAAAP// AQBjAIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA ; г) sin α = b a size 12{"sin" α = { {b} over {a} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbYGAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALUGAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAc2lu7AEA AAAA//8DAHMAaQBuAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGAAAAJUCAABhAgAAAgDOsd0A AAAAAP//AQCxA4wAAQAAAAAAiwABAAIAAAAfAIoAAQA8AAAAAwA2AAAACgBPcGVuU3ltYm9s AAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAABAIcA AQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAGgAAAJ4DAABhAgAAAQAAAD0ATwEAAAAA//8B AD0AjAABAAAAAACLAAEAAgAAAB8AigABAEIAAAADADwAAAAQAExpYmVyYXRpb24gU2VyaWYA AAAAAACmAQAAAAADAAAABQAAAAAAAgD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAXAAAAKwUAAHIBAAABAGLTAAAAAAD//wEAYgCM AAEAAAAAAIsAAQACAAAAHwCFAAEABQAAAAAAAAABhAABAAUAAAAAAAAAAIoAAQA8AAAAAwA2 AAAACgBPcGVuU3ltYm9sAAAAAAAApgEAAP//AAAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAA AAAAiAABAAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAABnAAEAEAAAABAFAADcAQAA GgYAAPABAACMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAArBQAAhAMAAAEAYdMAAAAAAP// AQBhAIwAAQAAAAAAlQABAAQAAAAAAAAAlgABAAIAAAAJAIwAAQAAAAAA .

• Для треугольника АВС , где АВ=8 , справедливо равенство:

а) cos B = 3 8 size 12{"cos" B = { {3} over {8} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQ8HAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAA4HAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY29zMgIA AAAA//8DAGMAbwBzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAOUCAABhAgAAAQBCAgEA AAAA//8BAEIAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wA AAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA7QMAAGECAAABAAAAPQBPAQAAAAD//wEA PQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJpZgAA AAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEA BQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAB6BQAAcgEAAAEAM9MAAAAAAP//AQAzAIwA AQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwAAAADADYA AAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAA AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAYAUAANwBAABn BgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNl cmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAAB AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHoFAACEAwAAAQA40wAAAAAA//8B ADgAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; б) cos B = 5 8 size 12{"cos" B = { {5} over {8} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQ8HAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAA4HAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY29zMgIA AAAA//8DAGMAbwBzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAOUCAABhAgAAAQBCAgEA AAAA//8BAEIAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wA AAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA7QMAAGECAAABAAAAPQBPAQAAAAD//wEA PQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJpZgAA AAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEA BQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAB6BQAAcgEAAAEANdMAAAAAAP//AQA1AIwA AQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwAAAADADYA AAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAA AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAYAUAANwBAABn BgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNl cmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAAB AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHoFAACEAwAAAQA40wAAAAAA//8B ADgAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; в) cos B = 3 5 size 12{"cos" B = { {3} over {5} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQsHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAAoHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY29zMgIA AAAA//8DAGMAbwBzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAOUCAABhAgAAAQBCAgEA AAAA//8BAEIAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wA AAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA7QMAAGECAAABAAAAPQBPAQAAAAD//wEA PQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJpZgAA AAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEA BQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAB6BQAAcgEAAAEAM9MAAAAAAP//AQAzAIwA AQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwAAAADADYA AAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAA AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAYAUAANwBAABj BgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNl cmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAAB AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHoFAACEAwAAAQA10wAAAAAA//8B ADUAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; г) cos B = 8 5 size 12{"cos" B = { {8} over {5} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAQ8HAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAA4HAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY29zMgIA AAAA//8DAGMAbwBzAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAIA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAOUCAABhAgAAAQBCAgEA AAAA//8BAEIAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5TeW1ib2wA AAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAAAAEAhwAB AAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAA7QMAAGECAAABAAAAPQBPAQAAAAD//wEA PQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBTZXJpZgAA AAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAAAQCHAAEA BQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAB6BQAAcgEAAAEAONMAAAAAAP//AQA4AIwA AQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwAAAADADYA AAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAA AACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAAYAUAANwBAABn BgAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0aW9uIFNl cmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAABAAIAAAAB AIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAAHoFAACEAwAAAQA10wAAAAAA//8B ADUAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= .

• Для треугольника АВС , где АВ=8 , справедливо равенство:

а) ctg B = 5 7 size 12{ ital "ctg"" B "= { {5} over {7} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAbEHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAALAHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQiDs AQAAAAD//wMAIABCACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAZBgAAcgEAAAEANdMAAAAAAP// AQA1AIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA/wUA ANwBAAAFBwAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAABkGAACEAwAAAQA30wAA AAAA//8BADcAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; б) {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAckAAADU AQAACAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAMgAAADTAQAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAJUAAQAEAAAAAAAAAJYAAQACAAAACQCMAAEAAAAAAA== ctg B = 5 4 size 12{ ital "ctg"" B "= { {5} over {4} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAcQHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAMMHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQiDs AQAAAAD//wMAIABCACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAAZBgAAcgEAAAEANdMAAAAAAP// AQA1AIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA/wUA ANwBAAAYBwAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAADQGAACEAwAAAQA00wAA AAAA//8BADQAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; в) ctg B = 4 7 size 12{ ital "ctg"" B "= { {4} over {7} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAcQHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAMMHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQiDs AQAAAAD//wMAIABCACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAA0BgAAcgEAAAEANNMAAAAAAP// AQA0AIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA/wUA ANwBAAAYBwAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAABkGAACEAwAAAQA30wAA AAAA//8BADcAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA= ; г) ctg B = 4 5 size 12{ ital "ctg"" B "= { {4} over {5} } } {} VkNMTVRGAQAxAAAAAAAAAAEAGwAAAAAAAAAAAAAAAAABAAAAAQAAAAEAAAABAAAAAcQHAADm AwAANAAAAJYAAQACAAAACQCLAAEAAgAAAP//gQABABAAAAAAAAAAAAAAAMMHAADlAwAAlQAB AAQAAAAAAAAAlgABAAIAAAAJAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlv biBTZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAACAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQAC AAAAAQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACAB0AAABqAAAAYQIAAAMAY3RnBAIA AAAA//8DAGMAdABnAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAHQAAALACAABhAgAAAwAgQiDs AQAAAAD//wMAIABCACAAjAABAAAAAACLAAEAAgAAAB8AigABADwAAAADADYAAAAKAE9wZW5T eW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAAAP8DAAAAAACIAAEAAgAA AAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAHIAAgAaAAAAjAQAAGECAAABAAAAPQBPAQAA AAD//wEAPQCMAAEAAAAAAIsAAQACAAAAHwCKAAEAQgAAAAMAPAAAABAATGliZXJhdGlvbiBT ZXJpZgAAAAAAAKYBAAAAAAMAAAAFAAAAAAAAAP8DAAAAAAAAAAAA/wMAAAAAAIgAAQACAAAA AQCHAAEABQAAAP////8AhgABAAQAAAAAAAAAcgACABcAAAA0BgAAcgEAAAEANNMAAAAAAP// AQA0AIwAAQAAAAAAiwABAAIAAAAfAIUAAQAFAAAAAAAAAAGEAAEABQAAAAAAAAAAigABADwA AAADADYAAAAKAE9wZW5TeW1ib2wAAAAAAACmAQAA//8AAAAABQAAAAAAAAD/AwAAAAAAAAAA AP8DAAAAAACIAAEAAgAAAAEAhwABAAUAAAD/////AIYAAQAEAAAAAAAAAGcAAQAQAAAA/wUA ANwBAAAYBwAA8AEAAIwAAQAAAAAAiwABAAIAAAAfAIoAAQBCAAAAAwA8AAAAEABMaWJlcmF0 aW9uIFNlcmlmAAAAAAAApgEAAAAAAwAAAAUAAAAAAAAA/wMAAAAAAAAAAAD/AwAAAAAAiAAB AAIAAAABAIcAAQAFAAAA/////wCGAAEABAAAAAAAAAByAAIAFwAAABkGAACEAwAAAQA10wAA AAAA//8BADUAjAABAAAAAACVAAEABAAAAAAAAACWAAEAAgAAAAkAjAABAAAAAAA=

8

7

Оценка работы с тестом

Взаимопроверка ответов теста

Вариант 1 Вариант 2

• В 1. Г
• Г 2. В
• В 3. Б
• Б 4. Г

закрепление

• В

• 1
• С 2 А
• 1 ) Найти ответы:
• 2 ) Найти
• 3 )Найти
• 4 )Найти
• 5 )Найти
• 6 )Найти

• Задание. Дан прямоугольный треугольник АВС с острым углом А и сторонами а = 4,

b = 3.Найдите:

1)Sin A =

Cos A =

2)Чему равно выражение:

Sin 2 A + Cos 2 A =

В

c

a

А

С

b

Ответы:

1. Ответ: Sin A = 4/5

Cos A = 3/5.

2. Ответ: Sin 2 A + Cos 2 A = 1.

Это основное тригонометрическое тождество.

sin 2 A + cos 2 A = 1

РАБОТА НА УРОКЕ

№ 593

Значения тригонометрических формул острых углов

Работа по чертежам

B C ABCD параллелограмм,

• ВЕ высота к стороне AD
• A E D АЕ=4см, Е D =5 см
• Найти площадь параллелограмма Проверим:
• Решение:
• 1) AD =...
• 2)
• 3) В E =...
• 4) S= ...
• Ответ:

Вычислить

РАБОТА НА УРОКЕ

№ 601, 602, 614, 623