Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, state the period of the function. y = cos 2x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, state the period of the function. y = sin 3x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, state the period of the function. \(y=\sin \frac{1}{3} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, state the period of the function. \(y=\cos \frac{1}{2} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the zeros and vertical asymptotes of the function. \(y=\frac{x-3}{x+4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the zeros and vertical asymptotes of the function. \(y=\frac{x+5}{x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the zeros and vertical asymptotes of the function. \(y=\frac{x+1}{(x-2)(x+2)}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the zeros and vertical asymptotes of the function. \(y=\frac{x+2}{x(x-3)}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, tell whether the function is odd, even, or neither. \(y=x^{2}+4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, tell whether the function is odd, even, or neither. \(y=\frac{1}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, identify the graph of each function. Use your understanding of transformations, not your graphing calculator. Graphs of one period of csc x and 2 csc x are shown.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, identify the graph of each function. Use your understanding of transformations, not your graphing calculator. Graphs of two period of 0.5 tan x and 5 tan x are shown.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, identify the graph of each function. Use your understanding of transformations, not your graphing calculator. Graphs of csc x and 3 csc 2x are shown.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, identify the graph of each function. Use your understanding of transformations, not your graphing calculator. Graphs of cot x and cot (x - 0.5) + 3 are shown.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = tan 2x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = - cot 3x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = sec 3x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = csc 2x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = 2 cot 2x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = 3 tan (x/2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = csc (x/2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 512, describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function. y = 3 sec 4x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, match the trigonometric function with its graph. Then give the Xmin and Xmax values for the viewing window in which the graph is shown. Use your understanding of transformations, not your graphing calculator. y = - 2 tan x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, match the trigonometric function with its graph. Then give the Xmin and Xmax values for the viewing window in which the graph is shown. Use your understanding of transformations, not your graphing calculator. y = cot x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, match the trigonometric function with its graph. Then give the Xmin and Xmax values for the viewing window in which the graph is shown. Use your understanding of transformations, not your graphing calculator. y = sec 2x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, match the trigonometric function with its graph. Then give the Xmin and Xmax values for the viewing window in which the graph is shown. Use your understanding of transformations, not your graphing calculator. y = - csc x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, analyze each function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x) = cot x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, analyze each function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x) = sec x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, analyze each function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x) = csc x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1720, analyze each function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x) = tan (x/2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. y = 3 tan x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. y = - tan x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. y = 3 csc x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. y = 2 tan x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. \(y=-3 \cot \frac{1}{2} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. \(y=-2 \sec \frac{1}{2} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. \(y=-\tan \frac{\pi}{2} x+2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2128, describe the transformations required to obtain the graph of the given function from a basic trigonometric graph. \(y=2 \tan \pi x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2934, solve for x in the given interval. You should be able to find these numbers without a calculator, using reference triangles in the proper quadrants. sec x = 2, \(0 \leq x \leq \pi / 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2934, solve for x in the given interval. You should be able to find these numbers without a calculator, using reference triangles in the proper quadrants. csc x = 2, \(\pi / 2 \leq x \leq \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2934, solve for x in the given interval. You should be able to find these numbers without a calculator, using reference triangles in the proper quadrants. \(\cot x=-\sqrt{3}, \quad \pi / 2 \leq x \leq \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2934, solve for x in the given interval. You should be able to find these numbers without a calculator, using reference triangles in the proper quadrants. \(\sec x=-\sqrt{2}, \quad \pi \leq x \leq 3 \pi / 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2934, solve for x in the given interval. You should be able to find these numbers without a calculator, using reference triangles in the proper quadrants. csc x = 1, \(2 \pi \leq x \leq 5 \pi / 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2934, solve for x in the given interval. You should be able to find these numbers without a calculator, using reference triangles in the proper quadrants. cot x = 1, \(-\pi \leq x \leq-\pi / 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3540, use a calculator to solve for x in the given interval. tan x = 1.3, \(0 \leq x \leq \frac{\pi}{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3540, use a calculator to solve for x in the given interval. sec x = 2.4, \(0 \leq x \leq \frac{\pi}{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3540, use a calculator to solve for x in the given interval. cot x = -0.6, \(\frac{3 \pi}{2} \leq x \leq 2 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3540, use a calculator to solve for x in the given interval. csc x = -1.5, \(\pi \leq x \leq \frac{3 \pi}{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3540, use a calculator to solve for x in the given interval. csc x = 2, \(0 \leq x \leq 2 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3540, use a calculator to solve for x in the given interval. tan x = 0.3, \(0 \leq x \leq 2 \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn The figure shows a unit circle and an angle t whose terminal side is in Quadrant III. (a) If the coordinates of point \(P_2\) are (a, b), explain why the coordinates of point \(P_1\) on the circle and the terminal side of angle \(t-\pi\) are \((-a,\ -b)\). (b) Explain

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Explain why it is correct to say y = tan x is the slope of the terminal side of angle x in standard position. P is on the unit circle.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Periodic Functions Let be a periodic function with period p. That is, p is the smallest positive number such that (x + p) = (x) for any value of x in the domain of . Show that the reciprocal 1/ is periodic with period p.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Identities Use the unit circle to give a convincing argument for the identity. (a) \(\sin (t+\pi)=-\sin t\) (b) \(\cos (t+\pi)=-\cos t\) (c) Use (a) and (b) to show that \(\tan (t+\pi)=\tan t\). Explain why this is not enough to conclude that the period of tangent is \(\pi\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Lighthouse Coverage The Bolivar Lighthouse is located on a small island 350 ft from the shore of the mainland as shown in the figure. (a) Express the distance d as a function of the angle x. (b) If x is 1.55 rad, what is d?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hot-Air Balloon A hot-air balloon over Albuquerque, New Mexico, is being blown due east from point P and traveling at a constant height of 800 ft. The angle y is formed by the ground and the line of vision from P to the balloon. This angle changes as the balloon travels. (a) Express the horizonta

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, find approximate solutions for the equation in the interval \(-\pi<x<\pi\). tan x = csc x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, find approximate solutions for the equation in the interval \(-\pi<x<\pi\). sec x = cot x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, find approximate solutions for the equation in the interval \(-\pi<x<\pi\). sec x = 5 cos x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, find approximate solutions for the equation in the interval \(-\pi<x<\pi\). 4 cos x = tan x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The function f(x) = tan x is increasing on the interval \((-\infty,\ \infty)\). Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False If x = a is an asymptote of the secant function, then cot a = 0. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice The graph of can be obtained by a horizontal shift of the graph of y = (A) - tan x. (B) - cot x. (C) sec x. (D) tan x. (E) csc x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice The graph of y = sec x never intersects the graph of y = (A) x. (B) \(x^2\). (C) csc x. (D) cos x. (E) sin x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice If \(k \neq 0\), what is the range of the function y = k csc x? (A) \([-k,\ k]\) (B) \((-k,\ k)\) . (C) \((-\infty,\ -k)\cup(k,\ \infty)\) (D) \((-\infty,\ -k]\cup[k,\ \infty)\) (E) \((-\infty,\ -1/k]\cup[1/k,\ \infty)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice The graph of y = csc x has the same set of asymptotes as the graph of y = (A) sin x. (B) tan x. (C) cot x. (D) sec x. (E) csc 2x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 57 and 58, graph both and g in the \([-\pi,\ \pi]\) by \([-10,\ 10]\) viewing window. Estimate values in the interval \([-\pi,\ \pi]\) for which > g. (x) = 5 sin x and g(x) = cot x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 57 and 58, graph both and g in the \([-\pi,\ \pi]\) by \([-10,\ 10]\) viewing window. Estimate values in the interval \([-\pi,\ \pi]\) for which > g. (x) = - tan x and g(x) = csc x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Graph the function (x) = - cot x on the interval \((-\pi,\ \pi)\). Explain why it is correct to say that is increasing on the interval \((0,\ \pi)\), but it is not correct to say that is increasing on the interval \((-\pi,\ \pi)\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Graph functions (x) = - sec x and \(g(x)=\frac{1}{x-(\pi / 2)}\) simultaneously in the viewing window \([0,\ \pi]\) by \([-10,\ 10]\). Discuss whether you think functions and g are equivalent.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Write csc x as a horizontal translation of sec x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Write cot x as the reflection about the x-axis of a horizontal translation of tan x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Television Coverage A television camera is on a platform 30 m from the point on High Street where the Worthington Memorial Day Parade will pass. Express the distance d from the camera to a particular parade float as a function of the angle x, and graph the function over the interval \(

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Whats in a Name? The word sine comes from the Latin word sinus, which means bay or cove. It entered the language through a mistake (variously attributed to Gerardo of Cremona or Robert of Chester) in translating the Arabic word jiba (chord) as if it were jaib (bay). This was due to the fact that the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Capillary Action A film of liquid in a thin (capillary) tube has surface tension \(\gamma\) (gamma) given by \(\gamma=\frac{1}{2} h \rho g r \sec \phi\), where h is the height of the liquid in the tube, \(\rho\) (rho) is the density of the liquid, \(g=9.8\mathrm{\ m}/\mathrm{\sec}^

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Advanced Curve Fitting A researcher has reason to believe that the data in the table below can best be described by an algebraic model involving the secant function: y = a sec (bx) Unfortunately, her calculator will do only sine regression. She realizes that the following