Trigonometric substitution
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Trigonometric substitution
A special type of u-substitution that generally involves substituting into an integral rather than another function because this enables the integral to be solved using trigonometric identities, double angle formulas, and half angle formulas, providing greater flexibility.
- Related Glossary Terms
Definite integral, Double Angle, Half angle, Indefinite integral, Trigonometric identities, U-substitution
- Index
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Trigonometric substitution
Trigonometric substitution replaces the variable of an integral with a trigonometric expression to simplify a radical. For example, x=a sin θ can turn a²−x² into a² cos²θ when a>0. The differential, bounds, and chosen angle interval must change consistently. The angle interval also determines signs when taking square roots, so √(cos²θ) cannot always be replaced by cos θ.
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