# Find the exact value of the following:

• Apr 7th 2013, 07:06 PM
boltage619
Find the exact value of the following:
cos^2 (pi/8) - 1/2 (a bit tricky)
• Apr 7th 2013, 07:36 PM
topsquark
Re: Find the exact value of the following:
Quote:

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
• Apr 7th 2013, 07:41 PM
boltage619
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.

Attachment 27860
• Apr 7th 2013, 07:45 PM
zhandele
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.
• Apr 7th 2013, 08:29 PM
ibdutt
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
• Apr 7th 2013, 08:40 PM
boltage619
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! :D