- #1

teme92

- 185

- 2

## Homework Statement

Given that cos([itex]\pi[/itex]/6) =[itex]\sqrt{}3[/itex]/2, use the double angle formula for the cosine function to find cos([itex]\pi[/itex]/12) and sin([itex]\pi[/itex]/12) explicitly.

## Homework Equations

cos(2x)=cos

^{2}x - sin

^{2}x

cos

^{2}x + sin

^{2}x = 1

## The Attempt at a Solution

So it wants me to find cos([itex]\pi[/itex]/12) which is half the angle of cos([itex]\pi[/itex]/6). So I called these cosx and cos 2x.

I then said [itex]\sqrt{}3[/itex]/2 = cos

^{2}x - sin

^{2}x

I used cos

^{2}x + sin

^{2}x = 1 and got sin

^{2}x on its own and subbed into the first formula and then got cosx on its own.

For sin([itex]\pi[/itex]/12) I subbed in sin

^{2}x = 1- cos

^{2}x and got sinx on its own.

Is this the correct method for finding the answers?

The inverse of cosx and sinx were [itex]\pi[/itex]/12 so I assume I am but not sure. I'd be thankful to anyone who could clear this up.