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Chapter 4: Problem 59

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

Short Answer

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

Step by step solution

01

Assess the given angle

The given angle is \(-160^{\circ}\). This angle is negative and less than \(360^{\circ}\).
02

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: \(-160^{\circ} + 360^{\circ}\).
03

Perform calculation

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

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