# Trigonometry

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Trigonometry is a branch of Mathematics and it is the study of the measure of the angles and the sides in a triangle using the trigonometric functions. In Trigonometry, there are 6 important functions and they are sine, cosine, tangent, cosecant, secant and cotangent of a given particular angle. Each trigonometric function has its own specific graph and there are also trigonometric identities and formulas which relate these functions together. Also based on different angles like half-angles, double-angles etc. we have the trigonometric formulas relating the functions together.

Example 1: If ‘θ’ is an angle in the first quadrant and sin(θ) = 3/5 and cos(θ) = 4/5, then what is the value of sin(2θ)?

Given sin(θ) = 3/5 and cos(θ) = 4/5

In order to find the value of sin(2θ), we can use the double-angle formula.

According to the trigonometric double-angle formula: sin(2θ) = 2 * sin(θ) * cos(θ)

Hence substituting the given values in the above formula we get:

sin(2θ) = 2 * 3/5 * 4/5

This gives: sin(2θ) = 24/25

Therefore the value of sin(2θ) = 24/25.

Example 2: If ‘θ’ is an angle in the first quadrant and sin(θ) = 3/5 and cos(θ) = 4/5, then what is the value of cos(2θ)?

Given sin(θ) = 3/5 and cos(θ) = 4/5

In order to find the value of cos(2θ), we can use the double-angle formula.

According to the trigonometric double-angle formula: cos(2θ) = cos2(θ) – sin2(θ)

Hence substituting the given values in the above formula we get:

cos(2θ) = (4/5)2 – (3/5)2 = 16/25 – 9/25

This gives: cos(2θ) = 7/25

Therefore the value of cos(2θ) = 7/25.