# Rational Expressions of Trigonometric Functions Expressions like are called rational expressions of sin and cos. Note that all the other trigonometric functions are rational functions of sin and cos. The main idea behind integrating such functions is the general substitution In order to have better feeling how things do work, remember the trigonometric formulas It is not hard to generate similar formulas for , , and from the above formulas. Therefore, any rational function will be transformed into a rational function of t via the above formulas. For example, we have where . Note that in order to complete the substitution we need to find dx as function of t and dt. Since , we get Now we are ready to integrate rational functions of sin and cos or at least transform them into integrating rational functions.

Check the following examples to see how this technique works: [Calculus]
[Geometry] [Algebra] [Trigonometry ]
[Differential Equations] [Complex Variables] [Matrix Algebra] S.O.S MATHematics home page

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