## anonymous 3 years ago cos theta = 4/5, 0˚< theta < 90˚ use the information given to find sin2theta, cos2theta, and tan 2theta

1. anonymous

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

2. anonymous

the identities?

3. anonymous

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4. anonymous

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. anonymous

do i plug in 4/5 where theta is?

6. anonymous

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

7. anonymous

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. anonymous

oh okay

9. anonymous

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

10. anonymous

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. anonymous

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

12. anonymous

use the numbers themselves, they are your sines and cosines

13. anonymous

okay thank you!

14. anonymous