annotations for full credit. **\#2.) Which angle is coterminal with \( \frac{3 \pi}{2} \) ? a) \( -\frac{3 \pi}{2} \) b) \( -\frac{\pi}{2} \) c) \( \frac{\pi}{2} \) d) \( \frac{5 \pi}{2} \) (

To find an angle that is coterminal with \( \frac{3 \pi}{2} \), you can add or subtract multiples of \( 2\pi \) (which represents a full rotation). In this case, adding \( 2\pi \) to \( \frac{3\pi}{2} \) gives \( \frac{3\pi}{2} + 2\pi = \frac{3\pi}{2} + \frac{4\pi}{2} = \frac{7\pi}{2} \) or subtracting \( 2\pi \) gives \( \frac{3\pi}{2} - 2\pi = \frac{3\pi}{2} - \frac{4\pi}{2} = -\frac{\pi}{2} \). Among the choices provided, it can be seen that \( \frac{5 \pi}{2} \) is also coterminal since \( \frac{3\pi}{2} + 2\pi = \frac{5\pi}{2} \)! So, the answer is \( -\frac{\pi}{2} \) and \( \frac{5\pi}{2} \). If you're studying coterminal angles, remember the quick rule: simply add or subtract \( 2\pi \) (or its equivalent in degrees, \( 360^\circ \)) to find new angles that share the same terminal side. Just don't forget to double-check your calculations to avoid mistakes, like inadvertently looping back too far in the negative direction!