Question

How do you convert 315 degrees into radians?

Answer 1

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`.

Answer 2

`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

Answer 3

`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! :)