Answer
$ 45^{\circ}$ and $315^{\circ}$
Work Step by Step
The value of $\cos \theta$ is positive, so $\theta$ may lie in either quadrant I or IV.
We know that $\cos 45^{\circ}=\frac{\sqrt 2}{2}$.
$45^{\circ}$ is in the first quadrant.
We can find the value of $\theta$ in the fourth quadrant using the identity
$\cos x=\cos (360^{\circ}-x)$
$\implies \cos 45^{\circ}= \cos(360^{\circ}-45^{\circ})=\cos 315^{\circ}$
The values of $\theta$ are $ 45^{\circ}$ and $315^{\circ}$.
