Radian Measure

Initially right triangles were used to define trigonometric ratios and angles were measured in degrees. But right triangles have limitations as they involve only acute angles. In degrees a full rotation corresponds to ◦ where the choice of was made thousands of years prior to the Babylonians. They might have application of chosen based on the number of days in a year.

But it does have the nice property of breaking into smaller angles like ◦ , ◦ , ◦ , ◦ and ◦ . In 17th century, trigonometry was extended to Physics and Chemistry where it required trigonometric functions whose domains were sets of real numbers rather than angles. This was accomplished by using correspondence between an angle and length of the arc on a unit circle. Such a measure of angle is termed as radian measure .

For theoretical applications, the radian is the most common system of angle measurement. Radians are common unit of measurement in many technical fields, including calculus. The most important irrational number π plays a vital role in radian measures of angles. Let us introduce the radian measure of an angle.

. Radian Measure Definition . The radian measure of an angle is the ratio of the arc length it subtends, to the radius of the circle in which it is the central angle. Consider a circle of radius r .

Let s be the arc length subtending an angle θ at the centre. Then, θ = arc length radius = s r radians. Hence, s = rθ .