Problem 67 - Precalculus Essentials

Question

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$-\frac{\pi}{50}$$

Step-by-Step Solution

Answer

The positive coterminal angle less than \(360^{\circ}\) or \(2 \pi\) is \(\frac{99\pi}{50}\) rad.

Step 1: Add 2π

The initial given angle is \(-\frac{\pi}{50}\). Add \(2\pi\) to this angle: \(-\frac{\pi}{50} + 2\pi = 2\pi - \frac{\pi}{50}\)

Step 2: Simplify

Simplify the above expression for ease of comparison: \(2\pi - \frac{\pi}{50} = \frac{100\pi - \pi}{50} = \frac{99\pi}{50}\)