Trigonametrik formulalar

FORMULALAR

1. Triganametrik ayniyatlar.

1. sin²α+cos²α=1

2. tgα∙ctgα=1

3. 1+tg²α=

4. 1+ctg²α=

5. tgα=

6. ctgα=

2. Trigonometrik funksiyalarni birinchisini ikkinchisi orqali ifodalash.

1) a)sinα=±√1-cos²α 2) a)cosα =±√1-sin²α

b)sinα= ± b)cosα =±

c)sinα= c)cosα=±

3) a)tgα=± 4) a)ctgα= ±

b)tgα= ± b)ctgα=±

c)tgα= c)ctgα=

3. Trigonometrik funksiyalarni yig’indisi va ayirmasi.

1) sin(α+β)=sinαcos β + cosαsin β

2) sin(α-β)=sinαcos β - cosαsin β

3) cos(α+β)=cosαcos β - sinαsin β

4) cos(α-β)= cosαcos β + sinαsin β

5) tg(α+β)=

6) tg(α-β)=

7) ctg(α+β)=

8) ctg(α-β)=

1) a)sinα= 2sin cos 2) cosα=cos²-sin

a) cosα=1-2sin²

b) sin2α=2sinαcosα cosα=2cos² -1

cosα=cos²α-sin²α

b) cosα=1-2 sin²α

cosα=2cos²α

3) tg²α= 4) ctg2α=

5. Yarim burchak.

1) sin =± 2) cos =±

3)tg ===±

4) ctg ===±

6. Darajani pasaytirish formulasi.

1) sin²α= 2) cos² α=

3) sin⁶ α+cos⁶ α=+cos⁴α

7. Trigonometrik funksiyani ko’paytmadan yig’indiga aylantirish.

1) sin α∙cos α= [ sin(α+β)+ sin(α-β)]

2) cos α∙cosβ= [ cos(α+β)-cos(α-β)]

3) sinα∙sinβ= [ cos(α-β)-cos(α+β)]

8. Triganametrik funksiyani yig’indidan ko’paytmaga aylantirish.

1

) sin α+sinβ=2sincos

2) sin α-sinβ=2sincos

3) cos α+cosβ=-2coscos

4) cos α-cosβ=-2sinsin

5) tg α+ctgβ=

6) tg α-ctgβ=

7) ctg α+ctgβ=

9. Keltirish formulalari.

1) a) sin(+α)=cos α 2) a) cos(+α)=sin α

b) sin (-α)= cos α b) cos(-α)=-sin α

c) sin(+α)=-cos α c) cos(+α)=sin α

d) sin (-α)= -cos α d) cos(-α)=-sin α

e) sin(π+ α)=-sin α e) cos(π+ α)=-cos α

f) sin (π- α)=-sin α f) cos(π- α)=-cos α