Question

Convert each angle to radian measure. $$ -120^{\circ} $$

Short answer

The angle \(-120^{\circ}\) in radians is \(-\frac{2}{3} \pi\).

Step-by-step solution

Write down the given angle and conversion factor

We are given the angle: \(-120^{\circ}\), and we know that \(1 radian = \frac{180}{\pi} degrees\).

Convert the angle to radians

To convert the angle from degrees to radians, we need to multiply the given angle in degrees by the conversion factor: \[-120^{\circ} \times \frac{\pi}{180^{\circ}}\]

Simplify

Now, we will simplify the expression by dividing -120 by 180 and multiplying the result by \(\pi\): \[-\frac{120}{180} \times \pi = -\frac{2}{3} \times \pi\]

Write the final answer

The angle \(-120^{\circ}\) converted to radians is: \[-\frac{2}{3} \pi\]