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

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