RADIAN MEASURE OF AN ANGLE
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.
Then,
θ = arc length / radius = s/r radians
Hence,
s = rθ
Points to Remember
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.
4.
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 our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Construction of Perpendicular from a Point on a Line
Oct 16, 19 11:02 AM
Construction of Perpendicular from a Point on a Line
-
Construction of Perpendicular Lines
Oct 16, 19 10:54 AM
Construction of Perpendicular Lines - Concept - Step by step explanation
-
Construction of Parallel and Perpendicular Lines
Oct 16, 19 10:48 AM
Construction of Parallel and Perpendicular Lines - Concept - Examples with step by step explanation
