91Ó°ÊÓ

Sketch at least one cycle of the graph of each cosecant function. Determine the period, asymptotes, and range of each function. $$ y=-2 \csc (x) $$

Graph \(y=x+\sin x\) on a graphing calculator for \(-100 \leq x \leq 100\) and \(-100 \leq y \leq 100 .\) Explain your results.

Sketch at least one cycle of the graph of each function. Determine the period and the equations of the vertical asymptotes. $$ y=2+\cot x $$

Graph \(y=x+\sin (50 x)\) on a graphing calculator for \(-10 \leq x \leq 10\) and \(-10 \leq y \leq 10\). Explain your results.

A weight hanging on a vertical spring is set in motion with an upward velocity of \(4 \mathrm{~cm} / \mathrm{sec}\) from its equilibrium position. A formula that gives the location of the weight in centimeters as a function of the time \(t\) in seconds is \(x=-\frac{4}{\pi} \sin (\pi t) .\) Find the period of the function and sketch its graph for \(t\) in the interval \([0,4]\) .

Write the equation of each curve in its final position. The graph of \(y=\cot (x)\) is shifted \(\pi / 3\) units to the right, stretched by a factor of \(2,\) then translated 2 units downward

Find the period and range of the function \(y=\cot (\pi x)\).

Find the equations for all vertical asymptotes for each function. $$ y=-\sec (x) $$

The graph of \(y=\cos (x)\) is shifted \(\pi\) units to the left, reflected in the \(x\) -axis, and then shifted 2 units upward. What is the equation of the curve in its final position?

At a distance of 500 feet from a giant redwood tree, the angle of elevation to the top of the tree is \(30^{\circ} .\) What is the height of the tree to the nearest foot?