Chapter 7: Analytic Trigonometry

Use the information given about the angle $0<\theta <2\mathrm{\pi }$, to find the exact value of $a.\sin 2\theta b.\cos 2\theta c.\sin \frac{\theta }{2}d.\cos \frac{\theta }{2}e.\tan \left(2\theta \right)f.\tan \frac{\theta }{2}$

$sec\theta =3,\sin \theta >0$

In Problems 13–24, find the exact value of each expression.

sin^-1 0

express each product as a sum containing only sines or only cosines

$\sin \vartheta \sin 2\vartheta$

Find the exact value of the expression:

$\cos \left(\frac{7\mathrm{\pi }}{12}\right)$

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.

${\sin }^{-1}\left[\sin \left(-\frac{8\mathrm{\pi }}{9}\right)\right]$

In Problems 11–34, solve each equation on the interval $0\le \theta \le 2\pi$.

$4{\cos }^2\theta =1$

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

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

Rewrite over a common denominator:

$\frac{1}{1-\cos \left(v\right)}+\frac{1}{1+\cos \left(v\right)}$

Establish the identity

$\frac{\sin (\alpha +\beta )}{\tan \alpha +\tan \beta }=\cos \alpha \cos \beta$

Find the exact value of the expression:

$\tan \left(\frac{7\mathrm{\pi }}{12}\right)$