Finding the cosine of an acute angle given the obtuse cosin

Question

I have the cosine of an obtuse angle and want to find the cosine of the acute angle:

i.e. I have $\cos{(\theta_{1})}$ how can I find $\cos{(\theta_{2})}$?

Answer 1

$\cos(\theta_2)=\cos(2\pi-\theta_1)=cos(-\theta_1)=\cos(\theta_1)$

Answer 2

Hint: $\theta_2=2\pi-\theta_1$.