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Question Video: Finding Positive and Negative Measures of Angles Coterminal to a given Angle Mathematics

Find one angle with positive measure and one angle with negative measure which are coterminal to an angle with measure 2πœ‹/3.

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Video Transcript

Find one angle with positive measure and one angle with negative measure which are coterminal to an angle with measure two πœ‹ over three radians.

Let’s consider the angle two πœ‹ over three radians. We could convert this into degrees by using the fact that πœ‹ radians is equal to 180 degrees. Two-thirds of 180 degrees equals 120 degrees, so two πœ‹ over three radians equals 120 degrees. However, we will keep our angle in radians in this question. As our angle is positive, we need to measure the angle in a counterclockwise direction from the initial side as shown.

We recall that coterminal angles share the same initial and terminal sides. This means that we need to find alternative ways to express the same angle. We can calculate coterminal angles by adding or subtracting two πœ‹ radians from the given angle. To find another positive angle, we need to keep measuring in the counterclockwise direction. This means that we need to add two πœ‹ radians to our angle. Two πœ‹ radians is equivalent to six πœ‹ over three radians. This means we need to add two πœ‹ over three and six πœ‹ over three. This is equal to eight πœ‹ over three radians. An angle with positive measure which is coterminal to an angle with measure two πœ‹ over three is eight πœ‹ over three radians.

In a similar way, we can find an angle with negative measure by moving in a clockwise direction. This means that we need to subtract two πœ‹ from our angle. Two πœ‹ over three minus six πœ‹ over three is equal to negative four πœ‹ over three. An angle with negative measure which is coterminal to an angle with measure two πœ‹ over three is negative four πœ‹ over three radians. The two angles are eight πœ‹ over three and negative four πœ‹ over three.

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