Trigonometric Substitutions

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Trigonometric Substitutions

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Trigonometric Substitutions Part II: Trigonometric Substitutions Monticello (Thomas Jefferson’s home), Alexandria, VA Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon, Siena College Photo by Vickie Kelly, 2004

We can use right triangles and the pythagorean theorem to simplify some problems. 1 These are in the same form.

We can use right triangles and the pythagorean theorem to simplify some problems. 1 This is a constant.

This method is called Trigonometric Substitution. If the integral contains , we use the triangle at right. If we need , we move a to the hypotenuse. If we need , we move x to the hypotenuse.

2 double angle formula

2 double angle formula

5 We can get into the necessary form by completing the square.

6 Complete the square:

Here are a couple of shortcuts that are result from Trigonometric Substitution: These are on your list of formulas. They are not really new. p