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In calculus, trigonometric substitutions provide an effective way to rationalize the radical forms $\sqrt{a^{2}-u^{2}}$ and $\sqrt{a^{2}+u^{2}}$ which in turn leads to the solution to an important class of problems. Involve such transformations. [Recall: $\sqrt{x^{2}}=|x| \text { for all real numbers } x .]$In the radical form $\sqrt{a^{2}-u^{2}}, a>0,$ let $u=a \sin x$ $-\pi / 2<x<\pi / 2 .$ Simplify, using a basic identity, and write the final form free of radicals. $\quad a \cos x$

$a \cos x$

Precalculus

Chapter 6

Trigonometric Identities and Conditional Equations

Section 1

Basic ldentities and Their Use

Trigonometry

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

07:16

In mathematics, a continuo…

04:09

00:59

In calculus, trigonometric…

01:06

01:14

02:15

In calculus, when integrat…

00:56

Use the given substitution…

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In mathematics, a continuous function is a function for which sufficiently s…

In calculus, trigonometric substitutions provide an effective way to rationa…

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