Question

corresponding degree measure for each angle.

1. what are the radian and degree measures of the angle of rotation from 0 to p in a counterclockwise direction?

find the equivalent radian or degree measure of each angle based on what is given:

1. 100° degrees = ___ radians
2. \frac{\pi}{5} radians = ___ degrees

Explanation:

Step1: Calculate the angle in radians for problem 15

The full - circle is \(2\pi\) radians or \(360^{\circ}\). The angle from \(O\) to \(P\) in the counter - clockwise direction is \(\frac{3}{4}\) of a full - circle.
The radian measure: \(\theta_{rad}=\frac{3}{4}\times2\pi=\frac{3\pi}{2}\) radians.
The degree measure: \(\theta_{deg}=\frac{3}{4}\times360^{\circ}=270^{\circ}\)

Step2: Convert \(100^{\circ}\) to radians (problem 16)

Use the conversion formula \(\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}\)
\(\theta_{rad}=100\times\frac{\pi}{180}=\frac{5\pi}{9}\) radians

Step3: Convert \(\frac{\pi}{5}\) radians to degrees (problem 19)

Use the conversion formula \(\theta_{deg}=\theta_{rad}\times\frac{180}{\pi}\)
\(\theta_{deg}=\frac{\pi}{5}\times\frac{180}{\pi}=36^{\circ}\)

Answer:

1. Radian measure: \(\frac{3\pi}{2}\), Degree measure: \(270^{\circ}\)
2. \(\frac{5\pi}{9}\)
3. \(36\)