Single Variable Calculus

Start Free Trial

Single Variable Calculus, Chapter 7, 7.6, Section 7.6, Problem 12

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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

If we let the values of right triangle be...

We know that $\displaystyle \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{x}{1} = x$

$\theta = \sin^{-1}(x)$

And,

$\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{\sqrt{1-x^2}}$

Thus, $\displaystyle \tan \left( \sin^{-1}(x) \right) = \tan (\theta) = \frac{x}{\sqrt{1-x^2}}$

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial