Question

How do you find `cos60` using the fundamental identities if you given `sin30=1/2`?

Answer 1

I would use the double angle formula:
`cos(2theta)=cos^2(theta)-sin^2(theta)`

and the fact that:
`sin^2(theta)+cos^2(theta)=1`
giving: `cos^2(theta)=1-sin^2(theta)`

So you get:
`cos(2theta)=cos^2(theta)-sin^2(theta)=`
`=1-sin^2(theta)-sin^2(theta)` substituting for:

for `theta =30°` and
`sin(30°)=1/2`
You get:
`cos(60°)=1-1/4-1/4=1/2`