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Chapter 4: Problem 30

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees. (a) \(120^{\circ}\) (b) \(-420^{\circ}\)

Short Answer

Expert verified
The two coterminal angles for \(120^{\circ}\) degrees are \(480^{\circ}\) and \(-240^{\circ}\). The two coterminal angles for \(-420^{\circ}\) degrees are \(300^{\circ}\) and \(-780^{\circ}\).

Step by step solution

01

Find coterminal angles for \(120^{\circ}\)

Coterminal angles can be found by adding or subtracting 360 degrees from the initial angle until the result is within the specified range (positive or negative). For positive coterminal angle, add 360 degrees: \(120^{\circ} + 360^{\circ} = 480^{\circ}\). For negative coterminal angle, subtract 360 degrees: \(120^{\circ} - 360^{\circ} = -240^{\circ}\). Thus, two coterminal angles for \(120^{\circ}\) are \(480^{\circ}\) and \(-240^{\circ}\).
02

Find coterminal angles for \(-420^{\circ}\)

As before, coterminal angles are found by adding or subtracting 360 degrees. For positive coterminal angle, since the initial value is negative, add 360 degrees until the result is positive: \(-420^{\circ}+ 360^{\circ}= -60^{\circ}\), since this is still negative, add 360 degrees once more: \(-60^{\circ} + 360^{\circ} = 300^{\circ}\). For negative coterminal angle, subtract 360 degrees: \(-420^{\circ} - 360^{\circ} = -780^{\circ}\). Thus, two coterminal angles for \(-420^{\circ}\) are \(300^{\circ}\) and \(-780^{\circ}\).

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