Question

an arc on a circle measures 250°. within which range is the radian measure of the central angle? 0 to $\frac{pi}{2}$ radians; $\frac{pi}{2}$ to $pi$ radians; $\frac{3pi}{2}$ to $2pi$ radians; $pi$ to $\frac{3pi}{2}$ radians

Explanation:

Step1: Recall degree - radian conversion formula

To convert degrees to radians, use the formula $\text{Radians}=\frac{\pi}{180}\times\text{Degrees}$.

Step2: Convert 250 degrees to radians

$\text{Radians}=\frac{\pi}{180}\times250=\frac{25\pi}{18}\approx 1.39\pi$.

Step3: Determine the range

Since $\pi\approx3.14$ and $\frac{25\pi}{18}\approx1.39\pi$, and $\pi < 1.39\pi<\frac{3\pi}{2}$ (because $\frac{3\pi}{2} = 1.5\pi$).

Answer:

$\pi$ to $\frac{3\pi}{2}$ radians