Chapter 7: Analytic Trigonometry

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

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

Write the trigonometric expression as an algebraic expression containing uand v

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

In Problem, use a calculator to find the value of each expression rounded to two decimal places.

$\mathrm{co}{t}^{-1}\left(-\sqrt{5}\right)$

solve each equation on the interval $0\le \theta <2\pi$

$\sin \theta -\sqrt{3}\cos \theta =1$

Establish each identity.

$\frac{\tan \alpha +\tan \beta }{cot\alpha +cot\beta }=\tan \alpha \tan \beta$

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

$6\sin x-e^x=2,x>0$

In Problems 91-93, find the real zeros of each trigonometric function on the interval $0\le \theta <2\pi$

$f\left(x\right)=\sin \left(2x\right)-\sin x$

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

$f\left(x\right)=\cos \left(2x\right)+\cos x$

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

$4\cos \left(3x\right)-e^x=1,x>0$

Establish each identity.

$(\tan \alpha +\tan \beta )(1-cot\alpha cot\beta )+(cot\alpha +cot\beta )(1-\tan \alpha \tan \beta )=0$