Question

convert the angle in radians to degrees.

-\frac{5\pi}{6}

-\frac{5\pi}{6}=\square^{circ} (type an integer or a decimal.)

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, use the formula: Degrees \(=\text{Radians}\times\frac{180^{\circ}}{\pi}\).

Step2: Substitute the given radian value

Given \(-\frac{5\pi}{6}\) radians. Substitute into the formula: \(-\frac{5\pi}{6}\times\frac{180^{\circ}}{\pi}\).
The \(\pi\) terms cancel out: \(-\frac{5}{6}\times180^{\circ}\).

Step3: Calculate the result

\(-\frac{5\times180^{\circ}}{6}=- 5\times30^{\circ}=-150^{\circ}\).

Answer:

\(-150\)