# How do you convert from 300 degrees to radians?

Feb 2, 2015

To do this conversion you have to think at what is a radian.
A radian is the angle that describes an arc of length equal to the radius.

Figure 1

To make our life easier let us make $r = 1$.

But what is the connection with degrees?
Consider an entire circle. We know that it spans 360° but how many radians?

If you try to draw them on top of your circle you'll find that you need a little bit more than 6 of the slices of figure 1 to cover your entire circle, i.e. 6 radians and a bit.

To get the exact number consider that an entire circle is a closed arc of length $2 \pi r$, the perimeter of the circle. If $r = 1$ you see that in an entire circle (that we know corresponds to 360° angle) we'll have $2 \pi = 6.28 \ldots$ radians!!!!

Now we have the key for our conversion:
360°=2pi
So:
if 360° is $2 \pi$
if I have 300° I'll have $x$ radians.
As a proportion:
360°:2pi=300°:x
and: x=2pi*300°/360°=5pi/3

If you want you can multiply the value of $\pi = 3.141 . .$ but I suggest to leave it as a fraction of pi.

Hope it helps