Problem 43 - Precalculus: A Concise Course

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.