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Chapter 4: Problem 51

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

Short Answer

Expert verified
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 by step solution

01

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}.
02

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}.

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