# How do you find the exact value of cos^-1(cos(-pi/4))?

${\cos}^{-} 1 \left(\cos \left(- \frac{\pi}{4}\right)\right) = \frac{\pi}{4}$
$\pi = {180}^{0} \therefore \frac{\pi}{4} = \frac{180}{4} = {45}^{0}$
${\cos}^{-} 1 \left(\cos \left(- \frac{\pi}{4}\right)\right) = {\cos}^{-} 1 \left(\cos \left(- 45\right)\right) = {\cos}^{-} 1 \left(\cos \left(45\right)\right)$ [since $\cos \left(- \theta\right) = \cos \theta$]. Let ${\cos}^{-} 1 \left(\cos 45\right) = \theta \therefore \cos \theta = \cos 45 \therefore \theta = {45}^{0} = \frac{\pi}{4} \therefore {\cos}^{-} 1 \left(\cos \left(- \frac{\pi}{4}\right)\right) = {45}^{0} = \frac{\pi}{4}$ [Ans]