# A Trigonometric Function

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There are 6 basic important trigonometric functions, and they are sine, cosine, tangent, cosecant, secant and cotangent of a given particular angle. Trigonometric functions are very useful because with the help of these functions we can calculate the measure of the sides and the angles of given triangles. These functions are related in many ways and the trigonometric identities and formulas give the relationship between these functions. Using their relationship, we can easily evaluate the angles and sides of a particular triangle.

Example 1: Given ‘θ’ in first quadrant, tan(θ) = 8/6. What is the value of the trigonometric function cos(θ)?

Given tan(θ) = 8/6

In a right angled triangle, to the given angle ‘θ’ -> tan(θ) = (opposite side)/ (adjacent side)

This means the given ratio (opposite side)/ (adjacent side) = 8/6.

So let the opposite side = 8x and adjacent side = 6x

Then according to Pythagorean theorem, (hypotenuse) = √[(8x)2 + (6x)2] = √(100x2)

This gives the hypotenuse = 10x

Since cos(θ) = (adjacent side)/ (hypotenuse)->cos(θ) = 6x/10x.

Therefore cos(θ) = 6/10

Example 2: Given‘θ’ in first quadrant,tan(θ) = 3/4. What is the value of the trigonometric function sin(θ)?

Given tan(θ) = 3/4

In a right angled triangle, to the given angle ‘θ’ -> tan(θ) = (opposite side)/ (adjacent side)

This means the given ratio (opposite side)/ (adjacent side) = 3/4

So let the opposite side = 3x and adjacent side = 4x

Then according to Pythagorean theorem, (hypotenuse) = √[(3x)2 + (4x)2] = √(25x2)

This gives the hypotenuse = 5x

Since sin(θ) = ( opposite side)/ (hypotenuse)-> sin(θ) = 3x/5x

Thereforesin(θ) = 3/5