LAW OF SINES AND COSINES AND OTHER APPLICATIONS OF TRIGONOMETRY

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Solution of triangles and trigonometry applications.

In a triangle ABC, the angles are denoted by the capital letters A, B, C and the lengths of sides opposite to these angles are denoted by a, b, c respectively. See the figure.
LAW OF SINES AND COSINES AND OTHER APPLICATIONS OF TRIGONOMETRY












Some important formulae regarding the sides and angles of a triangle are given as follows:



The law of  sines: In any triangle ABC




where R is the radius of the circumcircle of the triangle ABC. R is also known as the circumradius of the triangle.


The law of  cosines: In any triangle ABC

The law of cosines

Trigonometric ratios of half-angles in terms of the sides

Let 2s = a + b + c, so that s is the semi-perimeter of triangle ABC. Then,

Trigonometric ratios of half-angles in terms of the sides

Napier's anology: In any triangle ABC

Napier's anology











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