What radian measure is equivalent to $900°$?

• A. $\frac{9\pi }{4}$
• B. $\frac{5\pi }{2}$
• C. $5\pi$
• D. $2\pi$

Answer: (C)

Verified step by step guidance

1. Recall the fundamental relationship between degrees and radians: \(180^\circ = \pi\) radians.
2. To convert degrees to radians, use the formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
3. Apply this formula to convert \(900^\circ\) to radians: \(900 \times \frac{\pi}{180}\).
4. Simplify the fraction \(\frac{900}{180}\) by dividing numerator and denominator by their greatest common divisor.
5. Express the simplified fraction multiplied by \(\pi\) to get the radian measure equivalent to \(900^\circ\).