How do you convert 315 degrees into radians?

3 Answers
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

7/4 pi radians

Explanation:

To change from degrees to radians use the following formula:

degrees*(pi radians/180 degrees)

the (pi/180) 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:

315/180*pi radians

315 and 180 are both divisible by 45, so

315/180=7/4

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

7/4*pi radians = 7/4 pi radians

Mar 11, 2017

7/4 pi "radians"

Explanation:

The formula for converting degrees to radians is

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

rarr"radians"=(315*pi)/(180)

rarr"radians"=(cancel315^7*pi)/cancel(180)^4

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

Hope this helps! :)