# Thread: Find the exact value of the following:

1. ## Find the exact value of the following:

cos^2 (pi/8) - 1/2 (a bit tricky)

2. ## Re: Find the exact value of the following:

Originally Posted by boltage619
cos^2 (pi/8) - 1/2 (a bit tricky)
$cos \left ( \frac{\pi}{4} \right ) = \frac{\sqrt{2}}{2}$

Now, pi/8 is 1/2 of pi/4. What does the half angle formula for cosine give you?

-Dan

3. ## Re: Find the exact value of the following:

Well this is how my professor did it and i'm just confused on how she did it, she didn't use the half angle formula.

4. ## Re: Find the exact value of the following:

I'm not sure where you're coming from. Do you know the answer already, is this just a little puzzle for us?

If not, what do you know about trig that might help you? I notice we have a cos^2, which suggests a half-angle identity, and a pi/8 (half of a half of a half), which again suggest a half-angle identity. Do you know those identities? If you don't, you can find them online if necessary and work this out.

5. ## Re: Find the exact value of the following:

Use the half angle identities: cos 2A = 2(cosA)^2 - 1
cos pi/4 = 2 ( cos pi/8)^2 - 1 OR ( cos pi/8)^2 = [ cos pi/4 + 1 ]/ 2 Now just plugin the value of cos pi/4 and simplify

6. ## Re: Find the exact value of the following:

Cos 2A = 2cos^2 A -1 comes from the double-angle identity. And thanks for trying to help me out!