Problem

Simplify the expression. $ \sin(\tan^{-1} x) $

01:01

Problem 70 Hard Difficulty

Simplify the expression.

$ \tan (\sin^{-1} x) $

Answer

$\tan (y)=\frac{x}{\sqrt{1-x^{2}}}$

More Answers

02:13

Jeffrey P.

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

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Top Calculus 3 Educators

Catherine R.

Missouri State University

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University of Michigan - Ann Arbor

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Idaho State University

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Boston College

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Video Transcript

okay. We want to simplify this expression. Tangent of inverse sign of X in verse. Sign of X means the angle. Who signed his ex? I'm going to call that angle theta, so let's draw a reference triangle for data. So let's suppose this is angle Fada and we know it's sign is X. That means the opposite over high pot news is X so we could make the opposite X and the high pot noose. One X divided by one is X. Now we need the tangent of angle. Fada tangent is opposite over adjacent, so we need to find the length of the adjacent for right now I'm going to call it a and I'm going to use the Pythagorean theorem to find it. A squared plus X squared equals one squared, so a squared equals one minus X squared. So a is the square root of one minus X squared. All right, so now the tangent of that angle is the opposite X over the adjacent square root of one minus X squared

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Top Calculus 3 Educators

Catherine R.

Missouri State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Joseph L.

Boston College