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Trigonometry is the branch of Mathematics which consists of the 6 main trigonometric functions, which are sine, cosine, tangent, cosecant, secant, and cotangent of an angle. These trigonometric functions are used to write the trigonometric ratios, identities and different types of formulas based on the given angle. With the help of trigonometry, we can find the measure of the sides and angles of triangles and other geometric structures. These functions are also used to find the height of the buildings and also the distances from one location to another location.
 
Example 1: Given sin(θ) = 2/√5 and cos(θ) = 1/√5.  What is the value of tan(θ) and cot(θ)?

Given: sin(θ) = 2/√5, cos(θ) = 1/√5

The formula of tan(θ) is given as: tan(θ) = sin(θ)/ cos(θ)

This gives: tan(θ) = (2/√5)/ (1/√5) -> tan(θ) = (2/√5) * (√5/1) = 2/1.

Therefore, tan(θ) = 2/1.

Cotangent of the angle θ is also written as cot(θ) is the reciprocal of tan(θ).

This implies: cot(θ) = 1/tan(θ)

Therefore, cot(θ) = 1/ (2/1) = 1/2.

Hence the value of cot(θ) = 1/2

 Example 2: In right triangle PQR, side PR is the hypotenuse. If given the measure of angle Ras 30º and the length of side PR is 12m, then what is the length of side PQ?

Based on the question, here is the diagram.

The trigonometric function, sin(R) = (opposite side)/ (hypotenuse)

Therefore, sin(R) = PQ/PR      
      
This gives: sin(30)= PQ/ 12 -> 1/2= PQ/ 12

This implies: PQ= 12 * 1/2 = 6

Therefore the measure of the side, PQ= 6m.  

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