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Chapter 4: Problem 14

Sketch each angle in standard position. (a) \(\frac{5 \pi}{2}\) (b) 4

Short Answer

Expert verified
The sketch for \(\frac{5 \pi}{2}\) should show one full revolution around the circle plus another quarter rotation along the positive y-axis. For the angle 4, if assumed in radians, it should show a counter-clockwise rotation slightly over half the revolution around the circle; and if in degrees, it represents a very slight counter-clockwise rotation from the positive x-axis.

Step by step solution

01

Sketch the angle \(\frac{5 \pi}{2}\)

The angle \(\frac{5 \pi}{2}\) in radians exceeds \(2\pi\), which suggest more than one revolution around the circle is completed. In fact, it equals \(2\pi + \frac{\pi}{2}\), which represents one complete counterclockwise revolution around the circle and then a quarter of another revolution, or \(90^\circ\), ending up along the positive y-axis.
02

Sketch the angle 4

The angle 4 is a little trickier to sketch because it isn't immediately clear whether it is in degrees or radians. If we assume it's in radians, it roughly equals \(229.18^\circ\) (since \(1\) radian is approximately equal to \(57.3\) degrees), which if starting from the standard position, we rotate counter-clockwise over halfway around the circle, but less than a complete revolution. If it's in degrees, then it represents a very slight counter-clockwise rotation from the positive x-axis.

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