Question

1. for each angle measure, draw the angle in standard position and express its measure in both degrees and radians.

a. a full rotation ccw.
b. a half rotation cw.
c. one - quarter rotation ccw.

Explanation:

Step1: Recall the conversion formula

The conversion formula between degrees and radians is \(180^{\circ}=\pi\) radians.

Step2: Calculate for a full rotation CCW

A full rotation CCW is \(360^{\circ}\). Using the conversion formula \(\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}\), we have \(\theta_{rad}=\frac{\pi}{180}\times360 = 2\pi\) radians.

Step3: Calculate for a half rotation CW

A half - rotation CW: The degree measure is \(- 180^{\circ}\) (negative because it is clock - wise). Using the conversion formula \(\theta_{rad}=\frac{\pi}{180}\times(-180)=-\pi\) radians.

Step4: Calculate for one - quarter rotation CCW

A one - quarter rotation CCW: The degree measure is \(90^{\circ}\). Using the conversion formula \(\theta_{rad}=\frac{\pi}{180}\times90=\frac{\pi}{2}\) radians.

Answer:

a. \(360^{\circ},2\pi\) radians
b. \(-180^{\circ},-\pi\) radians
c. \(90^{\circ},\frac{\pi}{2}\) radians