How many radians is $-135°$?

• A. $-\frac{5\pi }{6}$
• B. $-\frac{3\pi }{4}$
• C. $-\frac{7\pi }{8}$
• D. $-\frac{2\pi }{3}$

Answer: (B)

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 angle \(-135^\circ\) into the formula: \(-135 \times \frac{\pi}{180}\).
3. Simplify the fraction \(\frac{135}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 45, resulting in \(\frac{3}{4}\).
4. Rewrite the expression as \(-\frac{3\pi}{4}\) radians after simplification.
5. Confirm that the radian measure is negative because the original degree measure is negative.