Answer the following. (a) Find an angle between 0 and 2pi that is coterminal with (31pi )/(12) (b) Find an angle between 0^circ and 360^circ that is coterminal with 1000^circ Give exact values for your answers. (a) square radians (b) square ^circ

<p> <br />1. Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. To find a positive angle that is coterminal with a given angle, you can add or subtract multiples of \( 2\pi \) (for radian measures) or 360° (for degree measures) until the result lies between 0 and \( 2\pi \) or 0° and 360°, respectively.<br />2. For part (a), the given angle is \( \frac{31\pi}{12} \). To find an angle between 0 and \( 2\pi \) that is coterminal with \( \frac{31\pi}{12} \), we subtract \( 2\pi \) (or \( \frac{24\pi}{12} \)) from \( \frac{31\pi}{12} \) to get \( \frac{7\pi}{12} \).<br />3. For part (b), the given angle is 1000°. To find an angle between 0° and 360° that is coterminal with 1000°, we subtract multiples of 360° from 1000° until the result lies in the desired range. Subtracting 720° (which is 2 times 360°) from 1000° gives 280°, which is the required coterminal angle.</p>