How do you convert from 300 degrees to radians?

1 Answer
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.
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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:
if 360° is #2pi#
if I have 300° I'll have #x# radians.
As a proportion:
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