Question

convert the angle θ = 180° to radians. express your answer exactly. θ = 180 π radians

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given degree value

We have \( \theta = 180^\circ \), so substituting into the formula: \( \theta = 180^\circ \times \frac{\pi}{180^\circ} \)

Step3: Simplify the expression

The \( 180^\circ \) in the numerator and denominator cancels out, leaving \( \theta = \pi \)

Answer:

\( \pi \)