Question

an arc on a circle measures 295°. the measure of the central - angle, in radians, is within which range? 0 to π/2 radians; π/2 to π radians; π to 3π/2 radians; 3π/2 to 2π radians

Explanation:

Step1: Convert degrees to radians

Use the formula $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. So for $\theta_{deg} = 295^{\circ}$, $\theta_{rad}=\frac{295\pi}{180}=\frac{59\pi}{36}\approx 5.15$ radians.

Step2: Compare with ranges

We know that $\frac{3\pi}{2}=\frac{6\pi}{4} = 4.71$ radians and $2\pi= 6.28$ radians. Since $4.71<5.15 < 6.28$, the angle is in the range $\frac{3\pi}{2}$ to $2\pi$ radians.

Answer:

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