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

Explanation:

Step1: Recall conversion formula

We know that $180^{\circ}=\pi$ radians. Let $x$ be the angle in radians for $270^{\circ}$. Then we set up a proportion $\frac{180^{\circ}}{\pi}=\frac{270^{\circ}}{x}$.

Step2: Cross - multiply and solve

Cross - multiplying gives $180x = 270\pi$. Then $x=\frac{270\pi}{180}$.

Step3: Simplify the fraction

Simplifying $\frac{270\pi}{180}$, we divide both the numerator and denominator by 90. So $x = \frac{3\pi}{2}$.

Answer:

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