Radian Measure of an Angle :
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.
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.
θ = arc length / radius = s/r radians
s = rθ
1. All circles are similar. Thus, for a given central angle in any circle, the ratio of the intercepted arc length to the radius is always constant.
2. When s = r, we have an angle of 1 radian. Thus, one radian is the angle made at the centre of a circle by an arc with length equal to the radius of the circle.
3. Since the lengths s and r have same unit, θ is unitless and thus, we do not use any notation to denote radians.
θ = 1 radian measure, if s = r
θ = 2 radian measure, if s = 2r
Thus, in general θ = k radian measure, if s = kr.
Hence, radian measure of an angle tells us how many radius lengths, we need to sweep out along the circle to subtend the angle θ.
5. Radian angle measurement can be related to the edge of the unit circle. In radian system, we measure an angle by measuring the distance travelled along the edge of the unit circle to where the terminal side of the angle intercepts the unit circle .
After having gone through the stuff given above, we hope that the students would have understood the radian measure of an angle.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit the following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Analytical geometry calculators
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Ratio and proportion shortcuts
Converting repeating decimals in to fractions