Question

convert the angle in radians to degrees.
-\frac{2\pi}{3}
-\frac{2\pi}{3}=\square^{circ} (type an integer or a decimal.)

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the angle in degrees and $R$ is the angle in radians.

Step2: Substitute the given value

Given $R =-\frac{2\pi}{3}$, substituting into the formula: $D=-\frac{2\pi}{3}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out. We have $D =-\frac{2\times180^{\circ}}{3}$. Then, $2\times180 = 360$, and $\frac{360}{3}=120$. So $D=- 120^{\circ}$.

Answer:

$-120$