Radians

Radian is a different unit system for measuring sizes of angles. It is the standard unit for angle size. Radians is the ratio of the arc length to the radius.

Eg. A semi circle with radius r would have an arc length of πr.

Angle in radians = arc length/radius = πr/r

= π

This tells us that π is equivalent to 180 degrees.

An angle of 1 radian means that the length of the radius is equal to the arc subtended on a circle.

The conversion is as follows:

360 degrees = 2π radians

1 degree = π/180 radians.

To convert degrees to radians we just multiply by π/180

To convert radians to degrees we just multiply by 180/π

The use of radians is extremely important as it allows certain trigonometric limits to work. This leads to certain identities in calculus to be true only if the units for angles used is radians.

When writing angles in radians the units “radians” is usually omitted.