How many radians is $342°$?

• A. $\frac{11\pi }{6}$
• B. $\frac{17\pi }{9}$
• C. $\frac{19\pi }{10}$
• D. $\frac{9\pi }{5}$

Answer: (C)

Verified step by step guidance

1. Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
2. Substitute the given degree measure into the formula: \(342^\circ \times \frac{\pi}{180}\).
3. Simplify the fraction \(\frac{342}{180}\) by finding the greatest common divisor (GCD) of 342 and 180 and dividing numerator and denominator by it.
4. Express the simplified fraction multiplied by \(\pi\) as your radian measure: \(\frac{\text{simplified numerator} \pi}{\text{simplified denominator}}\).
5. Write the final answer as a fraction in terms of \(\pi\), which represents the radian equivalent of \(342^\circ\).