Answer
$113.6^\circ$
Work Step by Step
Given equation is-
$\cos\theta$ = $-\frac{2}{5}$
The cosine function is one-to-one on the interval $[0, \pi]$ , so there is only one solution of the equation with $\theta$ between $0^\circ$ and $180^\circ$. To find that taking $\cos^{-1}$ of each side-
$\theta$ = $\cos^{-1}\frac{2}{5}$
Using calculator in degree mode-
$\cos^{-1}$ → $-2\div5$ = 113.578178478
i.e. $\theta$ = $\cos^{-1}(-\frac{2}{5}) \approx 113.6^\circ$
(Rounded to one decimal place)
