Question

How do you convert from 300 degrees to radians?

Answer 1

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 `2pir`, 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 `2pi=6.28...` radians!!!!

Now we have the key for our conversion:
`360°=2pi`
So:
if 360° is `2pi`
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