Problem 59 - Precalculus Essentials

Question

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$-160^{\circ}$$

Step-by-Step Solution

Answer

The positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle of \(-160^{\circ}\) is \(200^{\circ}\).

Step 1: Assess the given angle

The given angle is \(-160^{\circ}\). This angle is negative and less than \(360^{\circ}\).

Step 2: Find a positive coterminal angle

To find a positive coterminal angle, add \(360^{\circ}\) to the given angle. One could add \(360^{\circ}\) multiple times until obtaining a positive angle, however, in this case, adding it once should suffice as the absolute value of the negative angle is less than \(360^{\circ}\). Hence, the computation is: \(-160^{\circ} + 360^{\circ}\).

Step 3: Perform calculation

By adding \(-160^{\circ}\) and \(360^{\circ}\), the result yields \(200^{\circ}\).