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Chapter 4: Problem 43

Determine the quadrant in which each angle lies. (a) \(-132^{\circ} 50^{\prime}\) (b) \(-336^{\circ}\)

Short Answer

Expert verified
Both angles \(-132^{\circ} 50^{\prime}\) and \(-336^{\circ}\) lie in the fourth quadrant.

Step by step solution

01

Determine the Quadrant for Angle (a)

First, convert \(-132^{\circ} 50^{\prime}\) into degrees. Note that 1 degree equals 60 minutes. It becomes \(-132^{\circ} - \frac{50^{\prime}}{60}=-133^{\circ} 50^{\prime}\). Since this is negative, start at the positive x-axis and move clockwise (the direction for negative angles) 133 degrees 50 minutes. This puts the angle in the fourth quadrant.
02

Determine the Quadrant for Angle (b)

For \(-336^{\circ}\), no conversion is needed (there are no minutes in this angle). Since this angle is also negative, start at the positive x-axis and move clockwise (the direction for negative angles) 336 degrees. You would have completed nearly a full revolution (360 degrees), but fall 24 degrees short, which puts this angle once again in the fourth quadrant.

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