Tangent Formula

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Tangent of an angle is also represented as ‘tan(θ)’, where ‘θ’ is the angle measured in the first quadrant, second quadrant, third quadrant or the fourth quadrant in the coordinate plane. Tangent is one of the six important trigonometric functions and it is used to measure the sides or the angles of any given triangle. In a right angled triangle, tangent of an angle is the ratio of the opposite side to the adjacent side with respect to the particular angle and therefore it can also be written as: tan(θ) = (opposite side)/ (adjacent side).

Example 1: In the triangle ABC shown below, the side AB = 6m, BC = 8m. What is the tangent of the angle θ?

In triangle ABC, given angle ACB = θ     

The side opposite to the angle ‘θ’ is the opposite side.

This implies, side AB = Opposite side = 6m

The side adjacent to angle ‘θ’ is the adjacent side.

This implies, side BC = Adjacent side = 8m

Tangent of θ written as tan(θ) = (Opposite side)/ (Adjacent side)

Therefore tan(θ) = 6/8

Example 2: For an angle θ, given sin(θ) = 3/5 and cos(θ) = 4/5. What is the tangent of the angle θ?

Given: sin(θ) = 3/5 and cos(θ) = 4/5

Tangent of the angle θ is also written as ‘tan(θ)’.

tan(θ) is the ratio of sin(θ) and cos(θ).

This gives: tan(θ) = sin(θ)/ cos(θ)

This implies, tan(θ) = (3/5)/ (4/5) -> Now taking the reciprocal we get: (3/5) * (5/4)

This gives: tan(θ) = 3/4.

Therefore we get, tan(θ) = 3/4.

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