Question

convert the following angle from degrees to radians. express your answer in simplest form. 135°

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \)

Step2: Substitute the given degree value

We have \( 135^\circ \), so substitute into the formula: \( 135 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{135}{180} \). Both numerator and denominator are divisible by 45. \( \frac{135\div45}{180\div45} = \frac{3}{4} \)
So, \( 135^\circ \) in radians is \( \frac{3\pi}{4} \)

Answer:

\( \frac{3\pi}{4} \)