# How do you convert 315 degrees into radians?

Apr 18, 2015

With this proportion:

alpha_d:alpha_r=180°:pi

in whitch ${\alpha}_{d}$ is the measure of the angle in degree,

and ${\alpha}_{r}$ is the measure of the angle in radians.

So, if you want to convert an angle from radians in degree:

a_d=(alpha_r*180°)/pi

andif you want to convert an angle from degree to radians:

a_r=(alpha_d*pi)/(180°).

In our case:

a_r=(315°*pi)/(180°)=7/4pi.

Apr 18, 2015

$\frac{7}{4} \pi$ radians

#### Explanation:

To change from degrees to radians use the following formula:

degrees*(pi radians$/ 180$ degrees)

the $\left(\frac{\pi}{180}\right)$ means that for every $\pi$ radians you go around the unit circle, you've gone $180$ degrees.

So, taking our $315$ degrees and plugging into our equation we get:

$315$ degrees*(pi radians$/ 180$ degrees)

The "degrees" cancel out, then we are left with:

$\frac{315}{180} \cdot \pi$ radians

$315$ and $180$ are both divisible by $45$, so

$\frac{315}{180} = \frac{7}{4}$

So, then we just need to multiply by $\pi$ radians and we get:

$\frac{7}{4} \cdot \pi$ radians = $\frac{7}{4} \pi$ radians

Mar 11, 2017

$\frac{7}{4} \pi$ $\text{radians}$

#### Explanation:

The formula for converting degrees to radians is

color(brown)("radians"="degrees"*pi/180

$\rightarrow \text{radians} = \frac{315 \cdot \pi}{180}$

$\rightarrow \text{radians} = \frac{{\cancel{315}}^{7} \cdot \pi}{\cancel{180}} ^ 4$

color(green)(rArr7/4pi color(green)("radians"

Hope this helps! :)