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Chapter 4: Problem 24

Sketch each angle in standard position. (a) \(-\frac{7 \pi}{4}\) (b) \(\frac{5 \pi}{2}\)

Short Answer

Expert verified
The angle \(-\frac{7 \pi}{4}\) in standard position is equivalent to \(\frac{\pi}{4}\) while going clockwise. The angle \(\frac{5 \pi}{2}\) goes a bit beyond a whole round and ends up at \(\frac{\pi}{2}\) in the counter-clockwise direction.

Step by step solution

01

Plotting \(-\frac{7 \pi}{4}\)

Since the angle is negative, we will move in the clockwise direction from the positive x-axis. We can make things easier by converting \(-\frac{7\pi}{4}\) to a positive angle. Add \(2\pi\) to get \(\frac{\pi}{4}\) and then draw an angle of \(\frac{\pi}{4}\) radian in the counter-clockwise direction.
02

Plotting \(\frac{5 \pi}{2}\)

This time the angle is greater than \(2\pi\), so we have to go beyond an entire rotation. The value \(\frac{5 \pi}{2}\) after removing \(2\pi\) or \(4\pi/2\) gives \(\frac{\pi}{2}\). So, start from the positive x-axis and rotate counter-clockwise until you end up at the positive y-axis, which represents \(\frac{\pi}{2}\) radian.

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