Answer
$53.1^\circ$ and $126.9^\circ$
Work Step by Step
Given equation is-
$\sin\theta$ = $\frac{4}{5}$
To find one solution within domain, taking $\sin^{-1}$ of each side-
$\theta$ = $\sin^{-1}\frac{4}{5}$
Using calculator in degree mode-
$\sin^{-1}$ → $4\div5$ = 53.1301023542
i.e. $\theta$ = $\sin^{-1}(\frac{4}{5}) \approx 53.1^\circ$
(Rounded to one decimal place)
Another solution with $\theta$ between $0^\circ$ and $180^\circ$ is obtained by taking the supplement of the angle as this will be the reference angle of desired angle. Therefore-
Second solution with $\theta$ between $0^\circ$ and $180^\circ$
= $180^\circ - 53.1^\circ$ = $126.9^\circ$
So desired angles between $0^\circ$ and $180^\circ$ satisfying the given equation are $53.1^\circ$ and $126.9^\circ$
