Radian
Introduction
Introduction
In this chapter, we are going to explore a new way of measuring the size of angles. If you recall in primary school, you were introduced to the degrees unit (°). To recap, a full rotation is worth 360°. Radian is a different unit that is also used to measure the size of an angle. A full rotation is worth 2π radians. Hence we can say that:
2π radians = 360°
Animation of 1 Radian
Animation of 1 Radian
In the animation on the left, you will observe the construction of an angle of exactly 1 radian. It is the angle swept out by an arc with a length equal to its radius (1 unit in this example).
Conversion
Conversion
Angles can be converted from degree form to radian form and vice-versa using:
Angles can be converted from degree form to radian form and vice-versa using:
π radians = 180°
See formula on the right.
See formula on the right.
What are the advantages and disadvantages of using the radian compared to degree?
What are the advantages and disadvantages of using the radian compared to degree?
Next: Finding Arc Length
Next: Finding Arc Length
Side Track: Learn about another way to measure angles, the Gradian
Side Track: Learn about another way to measure angles, the Gradian