Trigonometry Online

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Trigonometry is one of the important and commonly used sections of Mathematics. Trigonometry is the study of measure of the angles and sides in triangles and other geometric structures. In trigonometry, right triangles are often used to calculate the measurements. But when required, the trigonometric functions are also extended to calculate the measurements of other types of triangles given the appropriate information. The trigonometric identities and formulas make the calculations much simpler and easy to analyze the measure of the angles and the sides in a triangle.

Example 1: In right triangle ABC, side AC is the hypotenuse. If given the measure of angle C as 45º and the length of side AC is 4m, then what is the length of side AB?

Based on the question, here is the diagram.

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

Therefore, sin(C) = AB/AC

This gives: sin(45)= AB/ 4 -> 1/√2= AB/ 4

This implies: AB= 4 * 1/√2 -> 4 * √2/ 2 = 2√2

Therefore the measure of the side, AB= 2√2m          

Example 2: Prove the given trigonometric identity: tan(x)/ cot(x) = [(sin(x)/cos(x)]2

Here let’s start with the left-hand side of the equation -> tan(x)/ cot(x)

We can also write the above expression as: tan(x)/ cot(x) = [sin(x/cos(x)]/ [cos(x)/sin(x)]

Here we can take the reciprocal of the denominator and this gives:

[sin(x)/ cos(x)] * [sin(x)/cos(x)]

This implies: [sin(x)]2/ [cos(x)]2 which can also be written as:

[sin(x)/ cos(x)]2 = right-hand side of the equation!

Hence proved!

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