**Relation between arc radius and angle**

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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**

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**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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