Chapter 7: Analytic Trigonometry

Use the information given about the angle $0<\theta <\frac{\pi }{2}$, to find the exact value of

$\tan \theta =\frac{4}{3},\mathrm{\pi }<\mathrm{\theta }<\frac{3\mathrm{\pi }}{2}$

Find the exact value of$\cos \left({\tan }^{-1}2\right)$.

True or False$\cos (\frac{\mathrm{\pi }}{2}-\theta )=\cos \theta$

In Problems 9–23, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.

${\sin }^{-1}\left(\sin \frac{3\mathrm{\pi }}{8}\right)$

$\tan ({\tan }^{-1}x)=xwhere\_\_\_\_\_.$

Express the product $\sin \left(4\theta \right)\cos \left(2\theta \right)$as a sum containing only sines or only cosines.

True or False Most trigonometric equations have unique solutions.

Use a calculator to evaluate the expression. Express angles in radians rounded to two decimal places.

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

Establish each identity.

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

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

$x^2=x+3\cos \left(2x\right)$