## abbyl94 2 years ago cos theta = 4/5, 0˚< theta < 90˚ use the information given to find sin2theta, cos2theta, and tan 2theta

1. satellite73

you need $$\sin(\theta)$$ so compute these do you know how to find it?

2. abbyl94

the identities?

3. satellite73

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4. alanli123

sin 2 theta = 2 sin theta cos theta cos 2 theta = 2 cos ^2 theta - 1 tan 2 theta = sin 2 theta / cos 2 theta

5. abbyl94

do i plug in 4/5 where theta is?

6. Azteck

If costheta=4/5 then sintheta= 3/5 $\sin2\theta=2\sin\theta \cos\theta$

7. satellite73

there is a picture of an angle whose cosine is $$\frac{4}{5}$$ you find the third side by pythagoras, or recalling the 3 - 4 - 5 right triangle this tells you $$\sin(\theta)=\frac{3}{5}$$

8. abbyl94

oh okay

9. abbyl94

so 2 sin theta = 2 sin 3/5 cos 4/5

10. satellite73

no do not make that mistake, it is a common one do not use $$\theta=\frac{4}{5}$$ use $$\cos(\theta)=\frac{4}{5}$$ so $\sin(2\theta)=2\times \frac{4}{5}\times \frac{3}{5}$

11. satellite73

no not the cosine and sine of those numbers, those numbers ARE the cosine and sine

12. satellite73

use the numbers themselves, they are your sines and cosines

13. abbyl94

okay thank you!

14. satellite73