91Ó°ÊÓ

In Exercises 9 and \(10,\) find all the trigonometric values of \(\theta\) with the given conditions. $$\tan \theta=-1, \quad \sin \theta<0$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=\sin (2 \pi t), \quad y=\cos (2 \pi t), \quad 0 \leq t \leq 1$$

In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(-1,4 / 3)$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=\sqrt[4]{-x}$$

In Exercises \(9-12,\) use a graph to find the zeros of the function. $$f(x)=e^{x}-4$$

In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=x^{3}+x$$

In Exercises \(11-14,\) determine (a) the period, (b) the domain, (c) the range, and (d) draw the graph of the function. $$y=3 \csc (3 x+\pi)-2$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=1+\frac{1}{x}$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=\cos (\pi-t), \quad y=\sin (\pi-t), \quad 0 \leq t \leq \pi$$

In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(0,-\sqrt{2})$$