Express the following angles into radians. \( \begin{array}{lllll}\text { (i) } 30^{\circ} & \text { (ii) }(60)^{\circ} & \text { (iii) } 135^{\circ} & \text { (iv) } 225^{\circ} & \text { (v) }-150^{\circ} \\ \text { (vi) }-225^{\circ} & \text { (vii) } 300^{\circ} & \text { (viii) } 315^{\circ} & & \end{array} \) Convert each of following to degrees.

To convert degrees to radians, you use the conversion factor that \(1^\circ = \frac{\pi}{180}\) radians. Here's how you would convert each of the given angles to radians: (i) \(30^\circ\) \[ 30^\circ \times \frac{\pi}{180} = \frac{30\pi}{180} = \frac{\pi}{6} \text{ radians} \] (ii) \(60^\circ\) \[ 60^\circ \times \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3} \text{ radians} \] (iii) \(135^\circ\) \[ 135^\circ \times \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4} \text{ radians} \] (iv) \(225^\circ\) \[ 225^\circ \times \frac{\pi}{180} = \frac{225\pi}{180} = \frac{5\pi}{4} \text{ radians} \] (v) \(-150^\circ\) \[ -150^\circ \times \frac{\pi}{180} = -\frac{150\pi}{180} = -\frac{5\pi}{6} \text{ radians} \] (vi) \(-225^\circ\) \[ -225^\circ \times \frac{\pi}{180} = -\frac{225\pi}{180} = -\frac{5\pi}{4} \text{ radians} \] (vii) \(300^\circ\) \[ 300^\circ \times \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3} \text{ radians} \] (viii) \(315^\circ\) \[ 315^\circ \times \frac{\pi}{180} = \frac{315\pi}{180} = \frac{7\pi}{4} \text{ radians} \] For converting radians to degrees, you use the conversion factor that \(1 \text{ radian} = \frac{180}{\pi}\) degrees. However, you did not ask for the conversion to degrees, so I have only provided the conversion to radians for each angle.