Problem 24 - Precalculus Essentials

Question

Convert each angle in radians to degrees. $$\frac{3 \pi}{4}$$

Step-by-Step Solution

Answer

The angle \( \frac{3 \pi}{4} \) in radians converts to \( 135 \) degrees.

Step 1: Know the conversion ratio

The conversion ratio from radians to degrees is \( \frac{180}{\pi} \) degrees.

Step 2: Multiply by the conversion ratio

Multiply the given angle \( \frac{3\pi}{4} \) by the conversion ratio provided in Step 1.

Step 3: Simplify the expression

Simplifying the expression gives \( \frac{3\pi}{4} \times \frac{180}{\pi} \), which simplifies to \( \frac{3 \times 180}{4} \) after cancelling out the \( \pi \) in the numerator and denominator of the fraction.

Step 4: Compute the final answer

Evaluating the fraction yields the final answer of \( 135 \) degrees.