Sine and Cosine Function Values Practice Test

A sound wave’s displacement is modeled by $y=\sin(\theta)$, where $\theta$ is the phase angle on the unit circle. At a particular time, the phase is $\theta=90^\circ=\pi/2$, measured counterclockwise from the positive $x$-axis. The unit circle has radius 1, so sine equals the $y$-coordinate. Use an exact value consistent with standard special angles. What is the sine of an angle measuring $\pi/2$ radians on the unit circle?

An AC circuit has a phase angle $\theta=45^\circ=\pi/4$ between voltage and current, modeled on the unit circle. The cosine of $\theta$ represents the in-phase component magnitude for a 1-unit signal. Angles are measured in radians for computation, but the setup also states degrees. Use standard unit-circle exact values, not rounded approximations. Using the unit circle, what is the cosine value for $\pi/4$?