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Chapter 4: Problem 57

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$395^{\circ}$$

Short Answer

Expert verified
The positive angle less than \(360^{\circ}\) that is coterminal with \(395^{\circ}\) is \(35^{\circ}\).

Step by step solution

01

Understand the Problem

The problem asks to find a positive angle which is less than \(360^{\circ}\) or \(2 \pi\) radians and is coterminal with \(395^{\circ}\). This requires understanding what coterminal angles are. Two angles are coterminal if they have the same initial side and terminal side.
02

Identify the Increment

In order to find an angle coterminal to \(395^{\circ}\) that is less than \(360^{\circ}\), first identify the increment that separates equivalent angle measurements. In this case, every full rotation of \(360^{\circ}\) brings us back to the same position.
03

Subtract the Increment

Subtract the increment identified in Step 2 from the given angle until a measurement less than \(360^{\circ}\) is reached. In this case, \(395^{\circ} - 360^{\circ} = 35^{\circ}\). Therefore, \(35^{\circ}\) is an angle that is coterminal with \(395^{\circ}\) and is less than \(360^{\circ}\).

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