Math 1022 Test 2

which statement is not true about sec? a) the function y=sec x obtains a local maximum at values of x for which the function y= cos x obtains a local maximum. b) the domain of y= sec x is {x/x does not equal (2n+1) pi/2, where n is an integer}. c) the range of y= sec x is identical to the range of y= csc x. d) the period of y= sec x is P= 2 pi.

a) the function y= sec x obtains a local maximum at values of x for which the function y= cos x obtains a local maximum

what is the range of y=tan-1 x? a) (-infinity, + infinity) b) (-π/2, π/2) c) (-π,π) d) (-π/4, π/4)

b) (-π/2, π/2)

if A, B, & C are constants such that B > 1, then which of the following statements is true about the graph y= A cos (BX-C)? a) the period is 2 pi and the phase shift is C. b) the period is 2 pi/B and the phase shift is C/B. c) the period is 2 pi and the phase shift is C/B. d) the period is 2 pi/B and the phase shift is C.

b) the period is 2 pi/B and the phase shift is C/B

if A, B, C, and D are constants, then which of the following statements is true about the graph of y= A cos (Bx-C) +D? a) the range is [-|A|-D, |A| +D]. b) the range is [-|A|+D, |A|+D]. c) the range is [-|A/B|+D, |A/B| +D]. d) the range is [-|A| -D, |A| -D].

b) the range is [-|A|+D, |A|+D]

which of the following is not a characteristic of the cosine function? a) the cosine function is an even function, which means that cos (-x) = cos x. b) the x-intercepts or zeros of the cosine function are of the form x= (2n+1)/ 2 pi where n is an integer. c) the cosine function obtains a relative maximum at x= 2 pi n where n is an integer. d) the y -intercept is 0.

d) the y-intercept is 0

if Θ= tan-1 x, then which of the following statements best describes angle Θ?

a) the angle Θis an angle satisfying the inequality -π/2 < Θ < π/2 having a terminal side lying in quadrant I, quadrant IV, or on the positive x-axis

what is the domain of the restricted cosine function whose inverse function is y= cos-1 x? a) [-π,π] b) [0,2π] c) [0,π] d) [-π/2, π/2]

c) [0, π]

if Θ= sin -1 x , then which of the following statements best describe angle Θ? a) the angle θ is an angle satisfying the inequality π less than or equal to θ less than or equal to 2π having a terminal side lying in quadrant III, quadrant IV, on the positive x-axis, on the negative x-axis, or the negative y-axis. b) the angle θ is an angle satisfying the inequality π/2 less than or equal to θ less than or equal to 3π/2 having a terminal side lying in quadrant II, quadrant III, on the positive y-axis, on the negative y-axis c) the angle θ is an angle satisfying the inequality 0 less than or equal to θ less than or equal to π having a terminal side lying in quadrant I, quadrant II, on the positive x-axis, on the positive y-axis, or on the negative x-axis d) the angle θ is an angle satisfying the inequality -π/2 less than or equal to θ less than or equal to π/2 having a terminal side lying in quadrant I, quadrant IV, on the positive x-axis, on the positive y-axis, or on the negative y-axis.

d) the angle Θ is an angle satisfying the inequality -π/2 < Θ ≤ π/2 having a terminal side lying in quadrant I, quadrant IV, on the positive x- axis, on the positive y- axis, or on the negative y-axis

if Θ= cos-1 x, then which of the following statements best describes angle Θ?

d) the angle Θ is an angle satisfying the inequality 0 ≤ Θ ≤ π having a terminal side lying in quadrant I, quadrant II, on the positive x-axis, on the positive y- axis, or the negative x-axis

which of the following statements best describes the graph of y= sin (x+C) where C > 0? a) the graph of y= sin (x+C) can be obtained by horizontally shifting each quarter point of y= sin (x) to the left C units. b) the graph of y= sin (x+C) can be obtained by horizontally shifting each quarter point of y= sin (x) vertically up C units. c) the graph of y= sin (x+C) can be obtained by horizontally shifting each quarter point of y= sin (x) to the right C units. d) the graph of y= sin (x+C) can be obtained by horizontally shifting each quarter point of y= sin (x) vertically down C units.

a) the graph of y= sin (x+c) can be obtained by horizontally shifting each quarter point of y= sin (x) to the left

which statements is true about cot? a) the domain of y= cot x is all real numbers except for values of x which cos x=0. b) the function y= cot x had infinitely many vertical asymptotes with equations x= n pi where n is an integer. c) the zeros of y= cot x are of the form n pi/2 where n is an integer. d) the principal cycle of the graph of y= cot x occurs on the interval (-pi/2, pi/2).

b) the function y= cot x has infinitely many vertical asymptotes with equations x= n pi where n is an integer

when sketching the graph of y= A tan (BX+C) +D which best describes how to determine the x- coordinate of the halfway points of the principal cycle? a) the x-coordinate of the hallway points are x= B/C and x= -B/C. b) the x-coordinates of each halfway point is located halfway between the x-coordinate of the center point and a vertical asymptote. c) the x- coordinate of each halfway point is located halfway between the x-coordinate of a local maximum point and the x-coordinate of a local minimum point. d) the x-coordinate of each halfway point is located halfway between the two vertical asymptotes.

b) the x- coordinate of each halfway point is located halfway between the x- coordinate of the center point and a vertical asymptote

which of the following statements is true? a) the zeros of y= tan x are all values of x for which cos x=0. b) the x-intercepts of y=tan x are the same as the x-coordinates of the center points of y= tan x. c) the function y= tan x is one- to- one. d) the domain of y= tan x is all real numbers except for values of x for which sin x= 0.

b) the x-intercept of y= tan x are the same as the x- coordinate of the center points of y= tan x

which of the following statements describes the definition of amplitude of a sine or cosine function? a) the amplitude is the minimum value of the sine or cosine function. b) the amplitude is the maximum value of the sine or cosine function. c) the amplitude is the measure of half the distance between the maximum and minimum values. d) the amplitude measures the distance between the maximum and minimum values.

c) the amplitude is the measure of half the distance between the maximum and minimum values

which of the following statements is not true about the function y= A cos (Bx)? a) the amplitude is |A|. b) the period is P= 2pi/B c) the range is [-|A|,|A|]. d) if B > 0 , the the function y= A cos (-Bx) is equivalent to the function y= -A cos (Bx).

d) if B > 0, then the function y= A cos (-Bx) is equivalent to the function y= -A cos (Bx)

which statement is not true about csc? a) the graph of y= csc x has infinitely many vertical asymptotes of the from x= n pi where n is an integer. b) the range of y= csc x is (-infinity, -1]U[1, infinity). c) the function y= csc x obtains a relative maximum at x= 3pi/ 2 +2pi n where n is an integer. d) the graph of y= csc x is symmetric about the y-axis.

d) the graph of y= csc x is symmetric about the y- axis

which is not a characteristic of the sine function? a) the x-intercepts or zeros of the sine function are of the form x=n pi where n is an integer. b) the y- intercept of the sine function is 0. c) the sine function is an odd function, which means that sin (-x)= - sin x. d) the sine function obtains a relative maximum at x= pi/2+pi n where n is an integer.

d) the sine function obtains a relative maximum at x= pi /2 + pi n where is an integer