Problem 20 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$-270^{\circ}$$

Step-by-Step Solution

Answer

The equivalent of -270 degrees in radians is \(-1.5\pi\) radians.

Step 1: Understand Conversion from Degrees to Radians

The conversion from degrees to radians involves multiplying the angle in degrees by \(\pi/180\). This derives from the fact that there are \(180^{\circ}\) or \(\pi\) radians in a half circle.

Step 2: Convert the Given Angle to Radians

To convert the given angle, -270 degrees, to radians, multiply it by \(\pi/180\): \(-270 \times (\pi/180) = -1.5\pi\) radians.

Step 3: Simplify the Result

In this case, no simplification is needed. The final answer in terms of multiples of \(\pi\) is \(-1.5\pi\).