Question

How do you find the exact values of cos15 (degrees) using the half angle formula?

Answer 1

I found: `cos(15°)=0.9659`

Explanation:

We use the half angle formula:
`cos^2(x)=1/2[1+cos(2x)]`
with `x=15°` and so `2x=30°`
so: `cos^2(15°)=1/2[1+cos(30°)]`
we know that `cos(30°)=sqrt(3)/2`
so:
`cos^2(15°)=1/2[1+sqrt(3)/2]`
`cos^2(15°)=(2+sqrt(3))/4`
square root both sides:
`cos(15°)=+-sqrt((2+sqrt(3))/4)=+-0.9659`
We choose the positive value.