## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 3 - Review Exercises - Page 135: 1

#### Answer

An angle with its vertex at the center of a circle that intercepts an arc on the circle double in length to the radius of the circle has a measure of 2 radians.

#### Work Step by Step

'An angle with its vertex at the center of a circle that intercepts an arc on the circle double in length to the radius of the circle has a measure of 2 radians.' To prove this, we assume the radius $r$ to be $x$. This means the arc length $s$ would then be $2x$. Substituting these values in $\theta=\frac{s}{r}$: $\theta=\frac{s}{r}=\frac{2x}{x}=2$ radians Hence proved that an angle with its vertex at the center of a circle that intercepts an arc on the circle double in length to the radius of the circle has a measure of 2 radians.

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