Problem 13 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$45^{\circ}$$

Step-by-Step Solution

Answer

The angle \(45°\) in radians is \(\pi /4\).

Step 1: Identify the conversion factor

The measure of an angle in radians is defined as the arc length along a unit circle. And, we know that the circumference of a unit circle is \(2\pi\). So, one revolution around a unit circle, or 360°, is equivalent to \(2\pi\) radians. Hence, 180° is equivalent to \( \pi \) radians. So, the conversion factor is \( \pi /180 \).

Step 2: Multiply by the conversion factor

Now, multiply the given angle in degrees by the conversion factor. For the angle of 45°, the conversion to radians would be \(45° \times ( \pi /180) = \pi /4 \) radians.