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# Applications Of Trigonometry

Trigonometry is the branch of mathematics which deals with Triangles and the relationship between the angles and sides of triangles.
Now we will see some applications of Trigonometry:
Some of the Applications of Trigonometry are given below:
Sine law – The law of sine (is also known as sine law, sine formula, or sine rule) is an equation which is used to compare the length of the sides of a triangle to its angle:
According to the sine law,
,
where x, y, and z are the length of the sides of a triangle, and X, Y, and Z are the opposite angles of a triangle.
And the reciprocal of above equation is:

Another application of trigonometry is:
Law of cosines: It is also said to be cosine formula or cosine rule. It is used to compare the lengths of the sides of a triangle to the cosine of one of its angle.
In the mathematical notation the cosine laws says that:
Z2 = x2 + y2 – 2xy cos ∂;
‘∂’ represents the angle between sides of lengths ‘x’ and ‘y’ and the opposite side length ‘z’.
Some other trigonometry applications are:
Suppose in a triangle if we know the two angles and one side of a triangle then SAA or ASA or laws of sine can be used to solve the triangle.
Now we will see how to find one side of a triangle:
Suppose we have a triangle XYZ and if X = 33 degree and ‘Y’ is 82.8 degree and ‘x’ is 43.9 inch. Then we find the value of ‘y’.
We know that the law of sine is:

Putting the values in the formula, we get:

or
Y =

## The Law of Sines to Solve Triangles

In mathematics, we study about Triangles, relationships between their sides and the angles between these sides; all these come under trigonometric. Among these Trigonometric Functions the sine function comes first in all. It gives the Ratio of the length of the side opposite to an angle (also called as perpendicular) to the length of the hypotenuse.

## The Law of Cosines

In mathematics, when we study about Triangles and the relationships between their sides and angles between these sides we use trigonometric Functions. Cosine function gives the Ratio of the length of side adjacent to an angle (also called as base) to the length of the hypotenuse.
Mathematically,
cos (theta) = adjacent / hypotenuse
The Law of Cosines also called Cos...Read More

## De Moivre's Theorem

De moivre’s theorem is used to calculate the roots of a complex for any power ‘n’, and the value of ‘n’ is Integer. As we know de moivres theorem is obtained from Euler’s equation. It is also used to join the Trigonometry to the Complex Number. The formula for demoivre s theorem is given by:
⇒ (cos p + isin p)n = cos (np) + I sin (np). This formula is used to join t...Read More

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