Coterminal Angles Determine TWO coterminal angles for the following degree or radian. \( \begin{array}{ll}\text { 5. } 85^{\circ} & \text { 6. } 375^{\circ} \\ \text { 7. } \frac{6 \pi}{7} & \text { 8. } \frac{10 \pi}{3}\end{array} \)

To find coterminal angles, you can add or subtract full rotations to the given angle. In degrees, a full rotation is \(360^\circ\), and in radians, it is \(2\pi\). Below are two coterminal angles for each given angle: --- **5. \(85^\circ\)** To find coterminal angles, add or subtract \(360^\circ\): 1. **Add \(360^\circ\):** \[ 85^\circ + 360^\circ = 445^\circ \] 2. **Subtract \(360^\circ\):** \[ 85^\circ - 360^\circ = -275^\circ \] **Coterminal Angles:** \(445^\circ\) and \(-275^\circ\) --- **6. \(375^\circ\)** To find coterminal angles, add or subtract \(360^\circ\): 1. **Add \(360^\circ\):** \[ 375^\circ + 360^\circ = 735^\circ \] 2. **Subtract \(360^\circ\):** \[ 375^\circ - 360^\circ = 15^\circ \] **Coterminal Angles:** \(735^\circ\) and \(15^\circ\) --- **7. \(\frac{6\pi}{7}\) radians** To find coterminal angles, add or subtract \(2\pi\): 1. **Add \(2\pi\):** \[ \frac{6\pi}{7} + 2\pi = \frac{6\pi}{7} + \frac{14\pi}{7} = \frac{20\pi}{7} \] 2. **Subtract \(2\pi\):** \[ \frac{6\pi}{7} - 2\pi = \frac{6\pi}{7} - \frac{14\pi}{7} = -\frac{8\pi}{7} \] **Coterminal Angles:** \(\frac{20\pi}{7}\) and \(-\frac{8\pi}{7}\) --- **8. \(\frac{10\pi}{3}\) radians** To find coterminal angles, add or subtract \(2\pi\): 1. **Add \(2\pi\):** \[ \frac{10\pi}{3} + 2\pi = \frac{10\pi}{3} + \frac{6\pi}{3} = \frac{16\pi}{3} \] 2. **Subtract \(2\pi\):** \[ \frac{10\pi}{3} - 2\pi = \frac{10\pi}{3} - \frac{6\pi}{3} = \frac{4\pi}{3} \] **Coterminal Angles:** \(\frac{16\pi}{3}\) and \(\frac{4\pi}{3}\) --- These coterminal angles share the same terminal side as the original angles when plotted in standard position.