Question

How do I find an angle that is not on the unit circle?

Answer 1

Use the angle sum and difference identities. See below.

Explanation:

The following identities may prove useful:

`sin(a+-b)=sinacosb+-cosasinb`

`cos(a+b)=cosacosb-sinasinb`

`cos(a-b)=cosacosb+sinasinb`

Basically, if you encounter an angle that's not on the unit circle, break it down into the sum or difference of two angles that are on the unit circle. Let's do an example with `cos(pi/12):`

`pi/12=pi/4-pi/6`

Thus,

`cos(pi/12)=cos(pi/4-pi/6)=cos(pi/4)cos(pi/6)+sin(pi/4)sin(pi/6)=sqrt(2)/2*sqrt(3)/2+sqrt(2)/2*1/2=sqrt(6)/4+sqrt(2)/4=(sqrt(6)+sqrt(2))/4`