Question

an arc on a circle measures $295^\circ$. the measure of the central angle, in radians, is within which range?
0 to $\frac{\pi}{2}$ radians
$\frac{\pi}{2}$ to $\pi$ radians
$\pi$ to $\frac{3\pi}{2}$ radians
$\frac{3\pi}{2}$ to $2\pi$ radians

Explanation:

Step1: Convert degrees to radians

To convert degrees to radians, use the formula: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$
$\text{Radians} = 295 \times \frac{\pi}{180} = \frac{59\pi}{36} \approx 1.639\pi$

Step2: Identify range of the value

First, convert the range bounds to decimals of $\pi$:

• $\frac{3\pi}{2} = 1.5\pi$
• $2\pi = 2\pi$

Since $1.5\pi < 1.639\pi < 2\pi$, the value falls in this interval.

Answer:

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