Radian

Concept

A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle. A radian is denoted by

When the length of arc AB is equal to radius OB ,

(1 radian)

Converting Radians into Degrees and Degrees back to Radians

We know that the circumference of a circle is 2pie r. When we are measuring the angle in radians, we are trying to find the ratio of the arc to the radius.

As a result, the angle subtended at O =

We also know that the number of degrees in a circle is

Hence,

 

or

It's not necessary to remember what 1 degree or 1 radian is. More importantly, you should understand the concept and derive it on the spot.

Scholar's Tip: When the unit of an angle is not specified, it usually means that the angle is in radians.

Examples

Radians into degrees

a) 2.63

So we simply multiply 2.63 with to obtain

(correct to the nearest 0.1 degrees) .

Degrees into Radians

b)

We multiply 0.01745 with 37 to obtain 0.64565 .

Interesting Tidbit: Radian is the S.I unit for measuring angles in a plane.

'Try it Yourself' Section

Give converting degrees to radians and vici versa a try by using the examples below.

a) 1.73 radian

b) 78 degrees

Return to Trigonometry Help or Basic Trigonometry .