Answer
$30.5^{\circ}$
Work Step by Step
Given-
$\tan\theta$ = $0.5890$ , $\theta$ belongs to Q I and $0^{\circ}\leq \theta\lt 360^{\circ}$
We will find reference angle of $\theta$ first, using calculator in degree mode by the $\tan^{-1}$ key with the value $0.5890$-
$0.5890$ → $\tan^{-1}$→→ 30.498085114
i.e. reference angle of $\theta$ = $30.5^{\circ}$ (to the nearest tenth of a degree)
The desired angle $\theta$ is in Q I, whose reference angle is $30.5^{\circ}$.
Therefore-
$\theta$ = $30.5^{\circ}$ ( for QI ref. angle of $\theta$ = $\theta$ as $0^{\circ}\leq \theta\lt 360^{\circ}$ )
