Problem 48 - Precalculus: A Concise Course

Question

Sketch each angle in standard position. (a) \(-750^{\circ}\) (b) \(-600^{\circ}\)

Step-by-Step Solution

Answer

The sketch for \(-750^{\circ}\) should have the terminal ray 30 degrees clockwise from the positive x-axis (equivalent to \(330^{\circ}\) in standard position). The sketch for \(-600^{\circ}\) should have the terminal ray 120 degrees counter-clockwise from the positive x-axis (equivalent to \(120^{\circ}\) in standard position).

Step 1: Understand negative angles in standard position

Since the given angles are both negative, we will be measuring clockwise from the positive x-axis. An angle of negative degree is identical to an angle of \((360-|degree|)^{\circ}\) measured in the opposite direction. So we need to calculate the angle we should rotate clockwise from the positive x-axis.

Step 2: Sketch the angle of \(-750^{\circ}\)

To find the equivalent positive angle for \(-750^{\circ}\), we add 360 to -750 until we get a positive angle. That gives us \(-750^{\circ} + 2\times360^{\circ} = -30^{\circ}\). This means that we measure 30 degrees clockwise from the positive x-axis.

Step 3: Sketch the angle of \(-600^{\circ}\)

To find the equivalent positive angle for \(-600^{\circ}\), we add 360 to -600 until we get a positive angle. That gives us \(-600^{\circ} + 2\times360^{\circ} = 120^{\circ}\). This means that we measure 120 degrees counter-clockwise from the positive x-axis (since 120 degrees is a positive measure).