Question

How do you convert `(5pi)/4` into degrees?

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`

and if you want to convert an angle from degree to radians:

`a_r=(alpha_d*pi)/(180°)`.

In our case:

`a_d=(5/4pi*180°)/pi=225°`.

Answer 2

2 pi radians = 360 degrees

Therefore:

pi radians = 180 degrees

This means that:

5/4 * pi radians = 5/4 * 180 degrees

And as a result:

5/4 pi radians = 225 degrees