Angles - Convert from Degrees or Radians to the Other

Trigonometry - How to Convert Degrees or Radians to the Other - How it Works - Video

Angles

Here we the table of the most radians and their angle in degrees.

If we take a look at π /4 + 3π /4, we find the slope of these points, we get π /180°.

If we take a look at 4π /3 + 5π /3 we find the slope of these points, we get π /180°.

What would happen if we put the degrees on top instead of the radians? What would happen if pick any two points? What does this relationship mean?

Well in order to convert degrees to radians we multiply degrees by π /180° and to convert radians to degrees we multiply radians by 180°/π .

Example 1

Example 1:

Here we have 60° and 85°.

In order to convert from degrees to radians we need to multiply by π /180°. Most of the time radians has a π on top so we need to have π in the numerator. Also we need the units (degrees) to cancel so we need degrees in the denominator to cancel with the degrees in our original angle.

60°

60° * π /180°

60°/180° * π

1/3 * π

π/3


Multiplied by π /180°

Moved degrees so one is top and one is bottom

Simplified.

Rearranged the terms.

85°

85° * π /180°

85°/180° * π

19/36 * π

19π/36


Multiplied by π /180°

Moved degrees so one is top and one is bottom

Simplified.

Rearranged the terms.

Example 2

Example 2:

Here we have 2π/3 and 5π/8.

In order to convert from radians to degrees we need to multiply by 180° / π. Most of the time degrees do not have a π so we need to cancel the π in our original angle and to do that we need π to be in the denominator. Also we need the units (degrees) to be added so we need degrees in the numerator so it is right next to the number.

2π/3

2π/3 * 180° / π

(2 * 180 / 3) * (π / π)

2 * 60°

120°


Multiplied by π /180°

Rearranged the terms.

Simplified.

Multiplied.

5π/8

5π/8 * 180° / π

(5 * 180 / 3) * (π / π)

5 * 45° / 2

112.5°


Multiplied by π /180°

Rearranged the terms.

Simplified.

Multiplied.

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