Question

what is the equivalent degree measure of $-\frac{2pi}{3}$ radians written in simplest terms?

• $-120^{circ}$
• $-\frac{360^{circ}}{3}$
• $-\frac{pi^{2}}{270}$
• $120^{circ}$

Explanation:

Step1: Use the conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
For \(-\frac{2\pi}{3}\) radians, the conversion is \( -\frac{2\pi}{3}\times\frac{180^{\circ}}{\pi}\).

Step2: Simplify the expression

Cancel out the \(\pi\) terms: \( -\frac{2}{3}\times180^{\circ}\).
Then calculate \( -\frac{2\times180^{\circ}}{3}\).
Since \(180\div3 = 60\), we have \( - 2\times60^{\circ}=-120^{\circ}\).

Answer:

\(-120^{\circ}\) (corresponds to the first option)