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: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).

Step2: Convert 295° to radians

Substitute 295° into the formula: \( 295 \times \frac{\pi}{180} = \frac{59\pi}{36} \approx 5.14 \) radians.

Step3: Analyze the ranges

• \( 0 \) to \( \frac{\pi}{2} \approx 1.57 \): \( 5.14 \) is not in this range.
• \( \frac{\pi}{2} \) to \( \pi \approx 3.14 \): \( 5.14 \) is not in this range.
• \( \pi \) to \( \frac{3\pi}{2} \approx 4.71 \): \( 5.14 \) is not in this range.
• \( \frac{3\pi}{2} \) to \( 2\pi \approx 6.28 \): \( 5.14 \) is in this range.

Answer:

\( \frac{3\pi}{2} \) to \( 2\pi \) radians (the last option: \( \frac{3\pi}{2} \) to \( 2\pi \) radians)