## anonymous 5 years ago use double angle formula to find the exact value of 2cos^2(3pie/8)-1

1. anonymous

Okay...

2. anonymous

Use the fact that$\cos{2 \theta}=\cos^2 \theta -\sin^2 \theta=2\cos^2 \theta -1$

3. anonymous

For$\theta = \frac{3\pi}{8}$$\cos 2 \theta =\cos \frac{3 \pi}{4}=\cos^2 \frac{3 \pi}{8}-1$The right-hand side is your expression. Now

4. anonymous

$\frac{3\pi}{4}$ lies in the second quadrant where cosine is negative. 3pi/4 is equivalent to 135 degrees. The cosine of 135 degrees is equal to the the negative cosine of 45 degrees, which has an exact value of $-\frac{1}{\sqrt{2}}$

5. anonymous

thank you!!!

6. anonymous

become a fan! would love the points

7. anonymous

what is the exact value of 2sin 157.5 cos 157.5

8. anonymous

This is an example of double angle for sine.$\sin 2 \theta = 2 \sin \theta \cos \theta$Here theta is 157.5, so 2 x theta = 315 degrees. 315 = 360 - 45 This lies in the fourth quadrant where sine is negative. You have sin(315)=-sin(45)= -1/sqrt(2) again.

9. anonymous

it says write the following expression as sin cos or tan of a double agent. then find the exact value