## aussy123 2 years ago Given: costheta= -4/5, sin x =-12/13 ,theta is in the third quadrant, and x is in the fourth quadrant; evaluate cos 2x. -119/169 119/169 -11/13

1. satellite73

you don't need the sine part

2. aussy123

then how do I start

3. terenzreignz

Two variables?

4. satellite73

$\cos(2x)=2\cos^2(x)-1$

5. tomhoffhim

|dw:1364529999084:dw|

6. satellite73

oh i see there is a $$\theta$$ and an $$x$$

7. aussy123

costheta= -4/5 I need cosx

8. satellite73

you are asked for $$\cos(2x)$$ where $$\sin(x)=-\frac{12}{13}$$

9. satellite73

$\cos(2x)=1-2\sin^2(x)$

10. aussy123

When I do it I get 169

11. aussy123

a denominator of 169

12. satellite73

there is no $$\theta$$ in your question

13. tomhoffhim

ok, I'll do it for you, give me a second, this is an easy question

14. aussy123

yea I had to put theta for that

15. tomhoffhim

satellite, you don't know what you're doing..

16. satellite73

$\cos(x)=1-2\sin^2(x)$ $\cos(x)=1-(\frac{-12}{13})^2$\

17. satellite73

18. satellite73

$\cos(2x)=1-(\frac{12}{13})^2$ $\cos(2x)=1-\frac{144}{169}$

19. satellite73

$\cos(2x)=\frac{25}{169}$

20. aussy123

I know, thats what I get, but it isnt a choice

21. satellite73

your question asks for $$\cos(2x)$$ and doesn't mention any $$\theta$$

22. aussy123

I know but that is what is already given

23. satellite73

oh damn i made a mistake!! sorry

24. tomhoffhim

I'm too lazy to do it but you need to draw the triangles and either use theta or x for the angle

25. aussy123

lol its okay, Ive made plenty

26. satellite73

$\cos(2x)=1-2\sin^2(x)$ $\cos(2x)=1-2\times (\frac{12}{13})^2$ $cos(2x)=1-2\times \frac{144}{169}$

27. satellite73

$\cos(2x)=1-\frac{288}{169}$$\cos(2x)=-\frac{119}{169}$

28. aussy123

Lol this is a lot of work, can you use this same formula for tan2Theta

29. aussy123

nvm. I found the formula, Thank you!