Chapter 7: Analytic Trigonometry

Write the trigonometric expression as an algebraic expression containing uand v

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

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

$x^2+3\sin x=0$

Establish each identity.

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

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

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

Write the trigonometric expression as an algebraic expression containing uand v

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

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

$x^2-2\sin \left(2x\right)=3x$

Establish each identity.

${(a\sin \theta +b\cos \theta )}^2+{(a\cos \theta -b\sin \theta )}^2=a^2+b^2$

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

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

In Problems 9–36, find the exact value of each expression.

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

Rewrite in terms of sine and cosine functions:$\tan \left(\theta \right)csc\left(\theta \right)$