Solving Trigonometric Equations in Context Practice Test

A rotating beacon points from north toward east. The angle $\theta$ is measured from the north direction, and the eastward component of the light’s direction is modeled by $\sin(\theta)$. If the beacon’s eastward component must be $0.6$, the model is

$$\sin(\theta)=0.6.$$

Which angle represents the correct solution within $0^\circ\le \theta\le 90^\circ$?

A pendulum’s horizontal displacement from its resting position is modeled by

$$x(\theta)=0.8\sin(\theta),$$

where $\theta$ is the angle (in radians) through which the pendulum has swung from the vertical. At a certain moment, the displacement is $x=0.4$ m. Which solution is valid given the situation if the swing angle is restricted to $-\frac{\pi}{2}\le \theta\le \frac{\pi}{2}$?