Chapter 7: Analytic Trigonometry

Find the exact solution of the equation.

$-3{\sin }^{-1}x=\mathrm{\pi }$

In Problems 79-90, find the exact value of each expression.

$\tan \left(2{\tan }^{-1}\frac{3}{4}\right)$

Establish each identity.

$\frac{\cos \theta +\sin \theta -{\sin }^3\theta }{\sin \theta }=cot\theta +{\cos }^2\theta$

Explain in your own words how you would use your calculator to find the value of$co{t}^{-1}10$.

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.

$\sin x+\cos x=x$

Use a graphing utility to solve the equation on the interval $0\le x\le 2\mathrm{\pi }$. Approximate any solutions rounded to two decimal places.

$2{\cos }^{-1}x+\mathrm{\pi }=4{\cos }^{-1}\mathrm{x}$

Write each trigonometric expression as an algebraic expression containing $u$and $v$. Give the restrictions required on $u$and $v$.

role="math" localid="1646564067411" $\cos \left({\cos }^{-1}u+{\sin }^{-1}v\right)$

Establish each identity.

$\frac{{(2{\cos }^2\theta -1)}^2}{{\cos }^4\theta -{\sin }^4\theta }=1-2{\sin }^2\theta$

In Problems 79-90, find the exact value of each expression.

$\sin \left(2{\cos }^{-1}\frac{4}{5}\right)$

Use a half-angle formula to find the exact value of $\sin 15°$. Then use a difference formula to find the exact value of $\sin 15°$. Show that the answers found are the same.