91Ó°ÊÓ

Prove each identity. $$\csc \theta+\sin (-\theta)=\frac{\cos ^{2} \theta}{\sin \theta}$$

Evaluate without using a calculator. $$\sin \left(\sin ^{-1} \frac{3}{5}\right)$$

Graph each of the following over the given interval. Label the axes so that the amplitude and period are easy to read. $$ y=-3 \sin 2 x,-2 \pi \leq x \leq 2 \pi $$

Evaluate without using a calculator. $$\cos \left(\cos ^{-1} \frac{5}{13}\right)$$

Prove each identity. $$\sec \theta-\cos (-\theta)=\frac{\sin ^{2} \theta}{\cos \theta}$$

Graph one complete cycle for each of the following. In each case, label the axes accurately and state the period and horizontal shift for each graph. $y=\tan \left(2 x+\frac{\pi}{2}\right

Graph each of the following over the given interval. Label the axes so that the amplitude and period are easy to read. $$ y=-3 \cos \frac{1}{2} x,-2 \pi \leq x \leq 6 \pi $$

Use your graphing calculator to graph each family of functions for \(-2 \pi \leq x \leq 2 \pi\) together on a single coordinate system. (Make sure your calculator is set to radian mode.) What effect does the value of \(A\) have on the graph? \(y=A \sin x\) for \(A=1,2,3\)

Evaluate without using a calculator. $$\cos \left(\cos ^{-1} \frac{1}{2}\right)$$

Sketch one complete cycle of each of the following by first graphing the appropriate sine or cosine curve and then using the reciprocal relationships. \(y=\csc \left(x+\frac{\pi}{4}\right)\)