How many radians are in a quarter of a circle?

• A. $2\pi$
• B. $\frac{\pi }{4}$
• C. $\pi$
• D. $\frac{\pi }{2}$

Answer: (D)

Verified step by step guidance

1. Recall that the total angle measure of a full circle in radians is given by the formula \$2\pi$ radians.
2. Understand that a quarter of a circle means dividing the full circle into 4 equal parts.
3. To find the radian measure of a quarter circle, divide the total radians of the full circle by 4: \(\frac{2\pi}{4}\).
4. Simplify the fraction \(\frac{2\pi}{4}\) by dividing numerator and denominator by 2, resulting in \(\frac{\pi}{2}\).
5. Therefore, the radian measure of a quarter of a circle is \(\frac{\pi}{2}\) radians.