Problem 28 - Precalculus Essentials

Question

Convert each angle in radians to degrees. $$-4 \pi$$

Step-by-Step Solution

Answer

The angle \( -4 \pi \) radians is equivalent to -720 degrees.

Step 1: Identify the given value

The given angle is \( -4 \pi \) radians.

Step 2: Use the radian to degree conversion

To convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \). Multiply the given angle by this factor: \( -4 \pi \cdot \frac{180}{\pi} \).

Step 3: Simplify the expression

\( \pi \) in the numerator and the denominator cancel out. Thus, the angle becomes \( -4 \cdot 180 \).

Step 4: Calculate the final result

Multiply 4 by 180 to get the final result in degrees. The result will be negative, as the angle was given as negative.