Question

what is the exact angle measure in radians? 495° ○ \\(\frac{4}{11}\pi\\) ○ \\(\frac{11}{4}\pi\\) ○ \\(\frac{11}{3}\pi\\) ○ \\(\frac{22}{3}\pi\\)

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given degree measure

We have \( 495^\circ \), so substitute into the formula: \( 495^\circ \times \frac{\pi}{180^\circ} \).

Step3: Simplify the fraction

First, find the greatest common divisor (GCD) of 495 and 180. The GCD of 495 and 180 is 45. Divide both the numerator and the denominator by 45: \( \frac{495 \div 45}{180 \div 45} = \frac{11}{4} \). So, \( 495^\circ \times \frac{\pi}{180^\circ} = \frac{11}{4}\pi \).

Answer:

\( \frac{11}{4}\pi \) (corresponding to the option \( \frac{11}{4}\pi \))