We can only use the sine and cosine functions of 30°, so we need to start with 60° = 2 × 30°.

We will use the result

cos 2α = cos² α − sin² α,

and the 30-60 triangle:

Now we proceed to find the exact value of cos60° using the ratios of 30°:

These exercises are really here for practice on the double angle formula. Of course, we could have found the value of cos60° directly from the triangle.