Welect your answer Which angle is coterminal to the angle \( \frac{3 \pi}{4} ? \) \( -\frac{3}{-\frac{3 \pi}{4}} \) \( -\frac{5 \pi}{4} \) \( -\frac{7 \pi}{4} \) \( -\frac{7 \pi}{4} \)

The angle \( \frac{3 \pi}{4} \) is in the second quadrant and coterminal angles are found by adding or subtracting multiples of \( 2\pi \). To find a coterminal angle in the form of a negative angle, we can subtract \( 2\pi \) (which is the same as subtracting \( \frac{8\pi}{4} \)) from our original angle: \[ \frac{3\pi}{4} - 2\pi = \frac{3\pi}{4} - \frac{8\pi}{4} = -\frac{5\pi}{4} \] This shows that the angle \( -\frac{5\pi}{4} \) is indeed coterminal with \( \frac{3\pi}{4} \). So the answer is \( -\frac{5 \pi}{4} \). As a fun fact, angles that differ by \( 2\pi \) radian measure share the same terminal side; this means they can essentially be thought of as the same angle in trigonometric terms. So the sides, sine, cosine, and other functions will all yield the same results for \( \frac{3\pi}{4} \) and \( -\frac{5\pi}{4} \)! If you’re delving into trigonometry, remember to keep a circle nearby (or maybe even draw one)! Visualizing angles and their positions can help anchor those coterminal angles in your mind. Consider creating a chart mapping out angles and their coterminal companions—it can turn into quite the colorful project!