91Ó°ÊÓ

Use the Tangent Half-Angle Identity and a Pythagorean identity to prove each identity. a. \(\tan \frac{A}{2}=\frac{\sin A}{1+\cos A}\) b. \(\tan \frac{A}{2}=\frac{1-\cos A}{\sin A}\)

Which expressions are equivalent? 1\. \(\cos \theta\) \(\quad\) II. \(\cos (-\theta)\) \(\quad\) III. \(\frac{\sin (-\theta)}{\tan (-\theta)}\) A. I and II only \(\quad\) B. II and III only \(\quad\) C. I and III only \(\quad\) D. \(I,III\) and III

In \(\triangle A B C, \angle B\) is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. $$ a=10, b=15 $$

If \(\theta\) is in Quadrant \(|\) and \(\tan \theta=\frac{5}{12},\) what is the value of \(\frac{\tan 4 \theta}{5}\) to the nearest hundredth? $$\begin{array}{llll}{\text { A. } 18.10} & {\text { B. } 0.33} & {\text { c. } 0.32} & {\text { D. }-23.90}\end{array}$$

Verify each identity. $$ \sin ^{2} \theta \tan ^{2} \theta+\cos ^{2} \theta \tan ^{2} \theta=\sec ^{2} \theta-1 $$

Find the \(x\) -intercepts of the graph of each function. $$ y=2 \cos \theta+1 $$

Simplify each trigonometric expression. $$ \frac{\cot ^{2} \theta-\csc ^{2} \theta}{\tan ^{2} \theta-\sec ^{2} \theta} $$

If \(\theta\) is in Quadrant \(|\) and \(\sin \theta=\frac{3}{5},\) what is an exact value of \(\sin 2 \theta ?\) $$ \begin{array}{llll}{\text { F. } \frac{9}{25}} & {\text { G. } \frac{24}{25}} & {\text { H. } \frac{6}{5}} & {\text { J. } 73.7}\end{array} $$

Which expressions are equivalent? \(I .-\tan \left(\frac{\pi}{2}-\theta\right)\) \(\quad\) Il. \(\cos (-\theta)\) \(\quad\) III. \(\tan \left(-\left(\frac{\pi}{2}-\theta\right)\right)\) F. I and II only \(\quad\) G. II and lll only \(\quad\) H. l and \(Il\) only \(\quad\) J. \(I,II,\) and III

In \(\triangle R S T, m \angle R=37^{\circ}, m \angle T=59^{\circ},\) and \(T S=12\) in. Find \(R S\)