Problem 25 - Precalculus Essentials

Question

Convert each angle in radians to degrees. $$\frac{7 \pi}{6}$$

Step-by-Step Solution

Answer

The angle \( \frac{7 \pi}{6} \) radians is equal to \( 210 \) degrees.

Step 1: Identify the angle in radians

The given angle is \( \frac{7 \pi}{6}\) radians

Step 2: Apply the conversion factor

To convert radians to degrees, we multiply our radians by the conversion factor which is \( \frac{180}{\pi}\). This gives us \( \frac{7 \pi}{6} * \frac{180}{\pi}\)

Step 3: Simplify the expression

After multiplying these values, the \(\pi\) in the numerator and denominator will cancel out and the expression simplifies to \( \frac{7 * 180}{6}\)

Step 4: Carry out the division

Performing the division gives us \(210\) degrees.