# How do you convert 270 degrees to radians?

Apr 8, 2018

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

#### Explanation:

We know:

color(red)(180^@ = pi \ \ \"radians"

Dividing by ${180}^{\circ}$:

$\frac{{180}^{\circ}}{{180}^{\circ}} = \frac{\pi}{{180}^{\circ}} \setminus \setminus \setminus \text{radians}$

${1}^{\circ} = \frac{\pi}{{180}^{\circ}} \setminus \setminus \setminus \text{radians}$

We are looking for ${270}^{\circ}$:

Multiply by ${270}^{\circ}$

${270}^{\circ} = \frac{{270}^{\circ} \pi}{{180}^{\circ}} \setminus \setminus \setminus \text{radians}$

We now reduce the fraction to its lowest terms:

$\frac{270}{180} = \frac{27}{18} = \frac{3}{2}$

So:

${207}^{\circ} = \frac{3 \pi}{2} \setminus \setminus \setminus \text{radians}$

The quick method for this is:

Divide the angle you have in degrees by 180, reduce it to its lowest terms, and then multiply by $\pi$:

$\therefore$

$\frac{270}{180} = \frac{3}{2} \times \pi = \frac{3 \pi}{2}$