Problem 51 - Precalculus: A Concise Course

Question

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees. (a) \(\theta=240^{\circ}\) (b) \(\theta=-180^{\circ}\)

Step-by-Step Solution

Answer

The positive coterminal angle for \(\theta=240^{\circ}\) is 600^{\circ} and the negative coterminal angle is -120^{\circ}. The positive coterminal angle for \(\theta=-180^{\circ}\) is 180^{\circ} and the negative coterminal angle is -540^{\circ}.

Step 1: Determine coterminal angles for \(\theta=240^{\circ}\)

To find the coterminal angles, add and subtract 360 degrees from the given angle. For the positive coterminal angle, calculate 240^{\circ}+360^{\circ}=600^{\circ}. For the negative coterminal angle, calculate 240^{\circ}-360^{\circ}=-120^{\circ}.

Step 2: Determine coterminal angles for \(\theta=-180^{\circ}\)

Again, add and subtract 360 degrees from the given angle. For the positive coterminal angle, calculate -180^{\circ}+360^{\circ}=180^{\circ}. For the negative coterminal angle, calculate -180^{\circ}-360^{\circ}=-540^{\circ}.