91Ó°ÊÓ

In Exercises \(7-12,\) one of \(\sin x, \cos x,\) and \(\tan x\) is given. Find the other two if \(x\) lies in the specified interval. $$ \tan x=\frac{1}{2}, \quad x \in\left[\pi, \frac{3 \pi}{2}\right] $$

In Exercises \(7-12,\) one of \(\sin x, \cos x,\) and \(\tan x\) is given. Find the other two if \(x\) lies in the specified interval. $$ \sin x=-\frac{1}{2}, \quad x \in\left[\pi, \frac{3 \pi}{2}\right] $$

In Exercises 5–30, determine an appropriate viewing window for the given function and use it to display its graph. $$ y=x^{1 / 3}\left(x^{2}-8\right) $$

Express the side length of a square as a function of the length \(d\) of the square's diagonal. Then express the area as a function of the diagonal length.

In Exercises \(5-12,\) solve the inequalities and show the solution sets on the real line. $$ -\frac{x+5}{2} \leq \frac{12+3 x}{4} $$

Express the edge length of a cube as a function of the cube's diagonal length \(d .\) Then express the surface area and volume of the cube as a function of the diagonal length.

In Exercises 13–16, find an equation for (a) the vertical line and (b) the horizontal line through the given point. $$ (-1,4 / 3) $$

In Exercises 13 and \(14,\) (a) write a formula for \(f \circ g\) and \(g \circ f\) and find the (b) domain and (c) range of each. $$ f(x)=\sqrt{x+1}, \quad g(x)=\frac{1}{x} $$

A point \(P\) in the first quadrant lies on the graph of the function \(f(x)=\sqrt{x}\) . Express the coordinates of \(P\) as functions of the slope of the line joining \(P\) to the origin.

Graph the functions in Exercises \(7-18 .\) What symmetries, if any, do the graphs have? Specify the intervals over which the function is increasing and the intervals where it is decreasing. $$ y=-4 \sqrt{x} $$