/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 58 Rewrite each angle in radian mea... [FREE SOLUTION] | 91Ó°ÊÓ

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Rewrite each angle in radian measure as a multiple of \(\pi\). (Do not use a calculator.) (a) \(315^{\circ}\) (b) \(120^{\circ}\)

Short Answer

Expert verified
In radian measures, \(315^{\circ} = \frac{7\pi}{4}\) and \(120^{\circ} = \frac{2\pi}{3}\)

Step by step solution

01

Convert 315 degrees to radians

To convert an angle from degrees to radians, we use the formula \(\text{radians} = \frac{\pi}{180} \times \text{angle in degrees}\). Applying this formula to the given angle \(\text{radians (for 315 degrees)} = \frac{\pi}{180} \times 315 = \frac{7\pi}{4}\).
02

Convert 120 degrees to radians

Using the same formula as above for conversion, we find that \(\text{radians (for 120 degrees)} = \frac{\pi}{180} \times 120 = \frac{2\pi}{3}\).

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