Trig review

[Jaina]

It's been so long since I took trig I really don't remember how to do this stuff. Here's the problem:

Find the fucntion value of cos^2 pi/12 using the double-angle formula.

All I remember is this:
(1+cos2(pi/12))/2

Where do I go from there?

 

[tkhunny]

cos(2A) = cos²A − sin²A = 2 cos²A − 1 = 1 − 2 sin²A

This leads to cos²A = ½(cos(2A) + 1)

If you use A = pi/12, you could be in business.

 

[Jaina]

Can I mulitply through the 2A and get pi/6, and use that? Or is that not okay to multiply the angle like that?

 

[Gene]

Yes, that was the purpose of the whole thing. They assume that "everyone" knows that cos(pi/6) (30°) is sqrt(3)/2 but doesn't know what cos(pi/12) is. This is a way of finding it.