Question

how many radians is 270°? give the exact answer in simplest form. radians

Explanation:

Step1: Recall degree-radian conversion

We know $180^\circ = \pi$ radians, so $1^\circ = \frac{\pi}{180}$ radians.

Step2: Convert $270^\circ$ to radians

Multiply $270$ by $\frac{\pi}{180}$:
$$270 \times \frac{\pi}{180} = \frac{270\pi}{180}$$

Step3: Simplify the fraction

Cancel common factors: $\frac{270}{180} = \frac{3}{2}$

Answer:

$\frac{3\pi}{2}$ radians