Relation Between Arc Radius And Angle


Relation between arc radius and angle



Arc length   =   [radius • central angle (radians)]

Arc length   =   circumference • [central angle (degrees) ÷ 360]



Proof of the trigonometric ratios of complementary allied angles

Two acute angles are complementary to each other if their sum is equal to 90°. In a right triangle the sum of the two acute angles is equal to 90°. So, the two acute angles of a right triangle are always complementary to each other.

Let ABC be a right triangle, right angled at B


If <ACB = ?, then <BAC = 90° – ? and hence the angles <BAC and <ACB are complementary  

For the angle ?, we have

Similarly, for the angle (90° – ?), we have

Comparing the equations in (1) and (2) we get,



Trigonometric Ratios of Complementary Angles






Examples: Evaluate  :  cos 56° / sin 34°

The angles 56° and 34° are complementary.

So, using trigonometric ratios of complementary angles, we have

cos 56°  =  cos (90° – 56°)  =  sin 34°

cos 56° / sin 34°  =  sin 34° / sin 34°  =  1  

Hence the value of cos 56° / sin 34° is 1.


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