Radians

There are two units of angles or the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet. We already know one of them, namely, degrees, but now, we are going to introduce a new unit called radians.

2𝛑 radians = 360 degrees

1 radian is around 57 degrees

Let’s try to convert between the two!

If I have an angle of 80 degrees, what is my angle in radians?

We would multiply 80 degrees by 2𝛑 radians and divide by 360 degrees. Diving by 360 degrees gets rid of the degrees unit (they cancel out) and multiplying by 2𝛑 adds in the radians unit.

80 degrees * 2𝛑 radians / 360 degrees = 1.4 radians or 0.44𝛑 radians (you do not have to multiply 𝛑 out and you can just keep it in your answer.

If I have an angle of 0.3𝛑 radians, what is my angle in degrees?

To convert to degrees, we would multiply by 360 degrees and divide by 2𝛑 radians.

0.3𝛑 radians * 360 degrees / 2𝛑 radians = 54 degrees

Let's try a quiz!