# 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

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