Chapter 7: Analytic Trigonometry

Establish each identity.

$\frac{1-2{\cos }^2\theta }{\sin \theta \cos \theta }=\tan \theta -cot\theta$

Consult three books on calculus and write down the

definition in each of $y=se{c}^{-1}x$and $y=\cos e{c}^{-1}x$. Compare

these with the definitions given in this book.

Write the trigonometric expression as an algebraic expression containing u and y

$\sin \left(\sin {}^{-1}u-\cos {}^{-1}v\right)$

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

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

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

$\sin x-\cos x=x$

Write the trigonometric expression as an algebraic expression containing u and v

$\sin \left({\tan }^{-1}u-{\sin }^{-1}v\right)$

If you are given the value of $\cos \theta$and want the exact value of role="math" localid="1646499973543" $\cos \left(2\theta \right)$, what form of the double-angle formula for $\cos \left(2\theta \right)$ is most efficient to use?

Establish each identity.

$\frac{1+\sin \theta +\cos \theta }{1+\sin \theta -\cos \theta }=\frac{1+\cos \theta }{\sin \theta }$

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

$x^2-2\cos x=0$

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

${\sin }^2\left(\frac{1}{2}{\cos }^{-1}\frac{3}{5}\right)$