What is radian measure of an angle?

Being an important topic of math, Radian is the most standard unit recognized for measurement of angles. Radian itself is an unit. It is equivalent to 180/π degrees where π is a constant approximately equal to 3.14. So let us define radian measure.

The radian measure of an angle is given by the angle acquired by a circular arc and the radii of endpoints of arc. As shown, the radian measure of an angle θ is given by the ratio of length of arc to the radius.
radian measure of an angle

Thus according to the radian measure definition, the radian measure of angles is given by

θ = l / r, where θ is the angle being measured in radians. It is often known as radian measure of a central angle.

Convert to radian measure from degrees

Let us now convert the angle in degrees to radians. For doing so, we need to multiply the degrees by the constant π/180. Converting it from grade, we need to multiply the grades by the constant π/200. Radian measure is recognized as derived unit of SI notation and popularly represented as 'rad'. A radian is approximately equal to 57.2 degrees when the radius is equal to the length of an arc. Now that we have studied all about radian measure, lets move on to examples.

(1) Convert 360 degrees to radians:

From the formula, 1° = π/180 radians, then 360° = ? It is given by 360 x π/180 = 2π. Thus 360 degrees equals 2π radians.

(2) Convert 400 grades to radians:

1 grade is equal to π/200 radians. So we need to multiply 400 by the ratio to get the angle in radians instead of grades. Doing so, we get 400 x π / 200 = 2π radians. Thus 400 grades equals 2π radians.

(3) Convert 360 degrees to grades:

From both the above examples, it is evident that 360 degrees equals 2π radians while 400 grades is also equal to 2π radians. Hence taking both at a time, 360 degrees equals 400 grades.

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