Problem 58 - Precalculus Essentials

Question

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$415^{\circ}$$

Step-by-Step Solution

Answer

The positive angle less than \(360^\circ\) or \(2\pi\) that is coterminal with \(415^\circ\) is \(55^\circ\).

Step 1: Determine the Given Angle

The given angle is \(415^\circ.\)

Step 2: Identify the Coterminal Angles

Coterminal angles can be found by adding or subtracting \(360^\circ\) or \(2\pi\) radians to the angle. In this case, we subtract \(360^\circ\) because the given angle is more than \(360^\circ\).

Step 3: Subtract \(360^\circ\) from the Given Angle

Subtracting \(360^\circ\) from the given angle, \(415^\circ - 360^\circ = 55^\circ.\)

Step 4: Confirm the Result

55 degrees is less than 360 degrees, so we have reached the solution for the exercise.