91Ó°ÊÓ

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {5 \pi / 8} & {2} & {? }\end{array}\)

In Exercises 1-4, (a) write a formula for the function and (b) use the formula to find the indicated value of the function. the area A of a circle as a function of its diameter d; the area of a circle of diameter 4 in.

In Exercises \(1-4,\) find the coordinate increments from \(A\) to \(B\). $$A(1,2), \quad B(-1,-1)$$

the surface area \(S\) of a cube as a function of the length of the cube's edge \(e\) ; the surface area of a cube of edge length 5 \(\mathrm{ft}\)

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {?} & {14} & {7 }\end{array}\)

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? $$x=-\sqrt{t}, \quad y=t, \quad t \geq 0$$

In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(3,2)$$

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? $$x=4 \sin t, \quad y=2 \cos t, \quad 0 \leq t \leq \pi$$

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

In Exercises 15 and 16, choose an appropriate viewing window to display two complete periods of each trigonometric function in radian mode. (a)(a) \(y=\sec x\) (b)\(y=\csc x\) (c)\(y=\cot x\)