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Properties of Trigonometric Functions

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## Trigonometry

Trigonometric functions are related with the properties of triangles. Some laws and formulas are also derived to tackle the problems related to triangles, not just right-angled triangles.

### Half Angle Formulas

With the introduction of the semiperimeter concept, the half angle identities of trigonometric functions can also be expressed in term of the semi-perimeter of a triangle or sides of a triangle.

The half angle formula for the sine funcion of an internal angle of a triangle can be obtained from the half angle identities of sine function by substituting the result of cosine function formula. Imply

The half angle formula for the cosine funcion of an internal angle of a triangle can be obtained from the half angle identities of cosine function by substituting the result of cosine function formula. Imply

The half angle formula for the tangent funcion of an internal angle of a triangle can be obtained from the half angle identities of tangent function by substituting the result of cosine function formula or from the half angle formula for sine and cosine functions directly. Imply

References

1. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science & Engineering, Blackie & Son Limited, HongKong
2. Ayres, F. JR, Moyer, R.E., 1999, Schaum's Outlines: Trigonometry, McGraw-Hill, USA
3. Hopkings, W., 1833, Elements of Trigonometry, Baldwin and Cradock, London

ID: 130600025 Last Updated: 2013/6/21 Revision: Ref:

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