How did they get from step a to step b?

[mpatryluk]

Homework Statement

In my calc book, they're calculating the integral of a specific parametric equation.

Homework Equations

The rest of the question is fine, I am just having trouble with these 2 lines.

I don't understand how cos^2(theta became 1/2(1+ cos2(theta))

Is this a trig relation that I am missing somewhere? If so, they should at least reference it at that step, as opposed to expecting us to memorize and recognize like 50 relationships... Otherwise, I'm lost...

As a side note, I've been looking through trig relations online but can't seem to find any mention of this one, so it makes me feel like I am missing something

 

[D H]

Hint: Expand cos(2θ).

 

[mpatryluk]

Hint: Expand cos(2θ).

Considering i don't even know how to begin to start to do that, this tells me i never learned trig properly. I must have really zoned out in quite a few classes when i was in school, lol.

Thank you

 

[jeppetrost]

This is really just one of those formulas you either remember or you don't. No one ever tells you all of them and expects you to remember.
Whenever you run into something like this, wikipedia or wolframalpha are your friends. Eg http://www.wolframalpha.com/input/?i=cos(2θ) (look under multiple argument formulas) or http://en.wikipedia.org/wiki/Trig_identities#Double-angle.2C_triple-angle.2C_and_half-angle_formulae .

If you want to calculate it, write cos (or sin) as exponentialfunctions and play around with those.

 

[mpatryluk]

This is really just one of those formulas you either remember or you don't. No one ever tells you all of them and expects you to remember.
Whenever you run into something like this, wikipedia or wolframalpha are your friends. Eg http://www.wolframalpha.com/input/?i=cos(2θ) (look under multiple argument formulas) or http://en.wikipedia.org/wiki/Trig_identities#Double-angle.2C_triple-angle.2C_and_half-angle_formulae .

If you want to calculate it, write cos (or sin) as exponentialfunctions and play around with those.

Ahh that's pretty useful for future reference. Thanks!