Reduction formulas

Definition

Reduction formulas rewrite trigonometric functions of multiple angles in terms of functions of simpler angles. They simplify complex expressions and are particularly useful for integration and solving equations.

5 Must Know Facts For Your Next Test

1. Reduction formulas often involve transforming trigonometric functions like $\sin(2x)$, $\cos(2x)$, and $\tan(2x)$ into simpler functions.
2. $\sin^2(x)$ can be rewritten using the reduction formula as $(1 - \cos(2x))/2$.
3. $\cos^2(x)$ can be rewritten using the reduction formula as $(1 + \cos(2x))/2$.
4. These formulas are derived from double-angle identities and help in integrating trigonometric functions.
5. Reduction formulas are also helpful in proving other trigonometric identities.

Review Questions

• How can you express $\sin^2(x)$ using a reduction formula?
• Which reduction formula would you use to simplify $\cos^4(x)$?
• Why are reduction formulas important when integrating trigonometric functions?

Related terms

Double-Angle Formulas: Formulas that express trigonometric functions of double angles, such as $\sin(2x) = 2 \sin(x) \cos(x)$.

Half-Angle Formulas: Formulas that express trigonometric functions of half-angles, such as $\sin(x/2) = \sqrt{(1 - \cos x)/2}$.

Trigonometric Identities: Equations involving trigonometric functions that are true for all values within their domains, such as $\sin^2(x) + \cos^2(x) = 1$.