Question

an arc on a circle measures 295°. 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 degree to radian

Use the conversion formula \( \theta_{rad}=\theta_{deg}\times\frac{\pi}{180}\).
For \( \theta_{deg} = 295^{\circ}\), we have \( \theta_{rad}=295\times\frac{\pi}{180}=\frac{59\pi}{36}\approx 5.15\) radians.

Step2: Compare with given ranges

• \(0\approx0\), \(\frac{\pi}{2}\approx1.57\), \(\pi\approx3.14\), \(\frac{3\pi}{2}\approx4.71\), \(2\pi\approx6.28\).
• Since \(4.71<5.15<6.28\) (i.e., \(\frac{3\pi}{2}<\frac{59\pi}{36}<2\pi\)).

Answer:

\(\frac{3\pi}{2}\text{ to }2\pi\text{ radians}\)