How many radians are in $200°$?

• A. $\frac{10\pi }{9}$
• B. $\frac{200\pi }{360}$
• C. $\frac{5\pi }{9}$
• D. $\frac{100\pi }{180}$

Answer: (A)

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. Substitute the given angle of \$200^\circ\( into the formula: \)200 \times \frac{\pi}{180}$.
4. Simplify the fraction \(\frac{200}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 20, resulting in \(\frac{10}{9}\).
5. Write the final expression for the angle in radians as \(\frac{10\pi}{9}\).