Question

select the correct choice that completes the sentence below.
to convert to degrees, multiply a radian measure by and simplify.

Explanation:

We know that the relationship between radians and degrees is \( \pi\) radians \( = 180^{\circ}\). To convert from radians to degrees, we want to cancel out the radian unit. If we have an angle \( \theta\) in radians, and we use the conversion factor \(\frac{180^{\circ}}{\pi}\), when we multiply \(\theta\) (in radians) by \(\frac{180^{\circ}}{\pi}\), the radian unit cancels out. For example, if \(\theta=\frac{\pi}{2}\) radians, then \(\frac{\pi}{2}\times\frac{180^{\circ}}{\pi}=90^{\circ}\).

Answer:

\(\frac{180^{\circ}}{\pi}\)