Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.1 Radian Measure - 3.1 Exercises - Page 104: 4

Answer

$\frac{180^{\circ}}{\pi}$

Work Step by Step

Using the circumference of a circle given by the formula $C=2\pi r$ and remembering that $\pi$ radians has a measure of a $180^{\circ}$ angle, we solve $180^{\circ}=\pi$ $radians$ for angles and for radians. Solving for degrees, $180^{\circ}=\pi$ $radians$ Dividing both sides by $180^{\circ}$. $\frac{180^{\circ}}{180}=\frac{\pi radians}{180}$ $1^{\circ}=\frac{\pi}{180}$ $radians$ Solving for radians, $180^{\circ}=\pi$ $radians$ Dividing both sides by $\pi$. $\frac{180^{\circ}}{\pi}=\frac{\pi radians}{\pi}$ $1 radian=\frac{180^{\circ}}{\pi}$ To convert to degrees, multiply a radian measure by $\frac{180^{\circ}}{\pi}$ and simplify.
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