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

For the angle θ, we have

Similarly, for the angle (90° – θ), 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.


KPSC Notes brings Prelims and Mains programs for KPSC Prelims and KPSC Mains Exam preparation. Various Programs initiated by KPSC Notes are as follows:- For any doubt, Just leave us a Chat or Fill us a querry––

Hope we have satisfied your need for KPSC Prelims and Mains Preparation

Kindly review us to serve even better

KPSC Mains Test Series 2020

20 Quality mock tests and GS Mains Notes

Mains Test Series and Notes

Mains Printed Notes (With COD)

KPSC Prelims Test Series 2020

24 Quality mock tests and GS Prelims Notes

Prelims Test Series and Notes

Prelims Printed Notes (With COD)

Subscribe to KPSC Notes

Never Miss any KPSC important update!

Join 1,939 other subscribers

error: Content is protected !!