Answer
$41.4^\circ$
Work Step by Step
Given equation is-
$\cos\theta$ = $\frac{3}{4}$
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-
$\theta$ = $\cos^{-1}\frac{3}{4}$
Using calculator in degree mode-
$\cos^{-1}$ → $3\div4$ = 41.4096221093
i.e. $\theta$ = $\cos^{-1}(\frac{3}{4}) \approx 41.4^\circ$
(Rounded to one decimal place)
