Question

Solve Cos^2(5pi/12) using double angle rules.
I've looked up double angle rules online but nothing has helped thus far

Answer 1

What double angle identities have you found so far that have cos^2 in them?

Answer 2

Cos^2(theta) - Sin^2(theta) = Cos2(theta)

Answer 3

A quick Google search yields http://www.sosmath.com/trig/douangl/douangl.html
The cosine double-angle is the first one listed.

Answer 4

Good. That's the general form; there are two other equivalent identities that cancel out either cos^2 or sin^2 using the Pythagorean identity, cos^2 + sin^2 = 1.

Answer 5

thanks im gonna try it again

Answer 6

I think using
\[\cos(2a)=2\cos^2(a)-1\] would be easiest.

Answer 7

If you have a labeled unit circle nearby, it should be pretty easy.

Answer 8

Let me know what you get so I can check my own work. ;-)

Answer 9

Cos^2(5pi/12)-Sin^2(5pi/12)=Cos2(5pi/12)

Answer 10

That will be a difficult equation to use..
The one I recommended would be less of a headache.

Answer 11

Cos(10pie/12) = 2Cos^2(5pi/12)-1

Answer 12

Yes, that'll work. It reduces to:\[\cos^2(5\pi/12)=\frac{1}{2}(1+\cos(5\pi/6)).\]

Answer 13

Cos(10pi/12) would be Cos(5pi/6) which would be equal to negative root 3 /2

Answer 14

Yeah, you should have it from there.

Answer 15

that's not all? I mean I know it has to be either 150 degrees or 210 degrees. What is the next step?

Answer 16

You're not solving for an angle, you're simplifying the expression.