1022 Test 2
D
If 3π /4< θ <5π /6, then which of the following mathematical statements is true A. tan^-1(tan θ )= θ B. sin^-1(sin θ )= θ C. sin^-1(sin θ )= θ D. cos^-1(cos θ )= θ
B
Which of the following statements is not true about the function y=A cos (Bx) A. The range is [-|A|, |A|] B. If B>0, then the function y=A cos (-Bx) is equivalent to the function y= - A cos (Bx) C. The period is P=2π/B D. The amplitude is |A|
D
Which of the following expressions is equivalent to the angle π/6 A. cos^-1(cos 7π/6) B. sin^-1(sin(-5π/6)) C. tan^-1(tan(-7π/6)) D. tan-1(tan(-5π/6))
B
Given the expression csc(cos^-1(1/2)), which of the following is not true? A. The expression csc(cos^-1(-1/2)) must be a value that is greater than 1 or less than negative 1 B. The expression csc (cos^-1(-1/2)) is equal to -2/√3 C. the expression cos^-1(-1/2) must be an angle with a terminal side that lies in Quadrant II D. The expression csc(cos^-1(-1/2)) is equivalent to the expression 1/sin(cos^-1(-1/2))
A
Which of the following is not a characteristic of the cosine function A. The y-intercept is 0 B. The cosine function is an even function, which means that cos (-x) = cos x C. the cosine function obtains a relative maximum at x=2πn where n is an integer D. The x-intercepts or zeros of the cosine function are the form x=(2n+1)/2(π) where n is an integer
C
Which of the following is not a characteristic of the sine function? A. the x-intercepts or zeros of the sine function are of the form x=nπ where n is an integer B. The sine function is an odd function, which means that sin (-x)= - sin x C. The sine function obtains a relative maximum at x= π /2+πn where n is an integer D. The y-intercept of the sine function is 0
D
Which of the following statements describe the definition of amplitude of a sine or cosine function A. the amplitude measures the distance between the maximum and minimum values B. The amplitude is the maximum value of the sine or cosine function C. The amplitude is the minimum value of the sine of cosine function D. The amplitude is the measure of half the distance between the maximum and minimum values
D
Which of the following statements is not true A. The range of y=csc x is (-∞ , -1]U[1, ∞ ) B. The graph of y=csc x has infintely many vertical asymptotes of the form x=nπ C. the function y=csc x obtains a relative maximum at x 3π/2 + 2πn where n is an integer D. The graph of y=csc x is symmetric about the y-axis
B
If A, B, and C are constants such that B>1, then which of the following statements is true about the graph of y=A cos (Bx-C) A. the period of 2π and the phase shift is C B. the period is 2π/B and the phase shift is C/B C. the period is 2π and the phase shift is C/B D. The period is 2π/B and the phase shift is C
A
If θ = cos^-1(x), then which of the following statements describes angle θ A.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 on the negative x-axis B.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 C. The angle θ is an angle satisfying the inequality π/2 ≤ θ ≤ 3π/2 having a terminal side lying in Quadrant II, Quadrant III, on the positive y-axis, on the negative x-axis, or on the negative y-axis D. The angle θ is an angle satisfying the inequality π ≤ θ ≤ 2π having a terminal side lying in Quadrant III, Quadrant IV, on the positive x-axis, on the negative x-axis, or on the negative y-axis
D
What is the domain of the restricted cosine function whose inverse function is y= cos^-1(x) A. [-π /2, π /2] B. [-π , π ] C. [0, 2π ] D. [0, π ]
B
What is the range of y=tan^-1(x) A. (-π /4, π /4) B. (-π /2, π /2) C. (-∞ , ∞ ) D. (-π , π )
C
When sketching the graph of y=A tan (Bx+C) +D which of the following best describe how to determine the x-coordinates of the halfway points of the principle cycle? A. 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 B. the x-coordinate of the halfway points are x=B/C and x= -B/C C. the x-coordinate of each halfway point is located halfway between the x-coordinate of the center point and a vertical asymptotes D. The x-coordinate of each halfway point is located halfway between the two vertical asymptotes
C
if y=sin(Bx) where B>0, then which of the following statements is true A. The period of y=sin(Bx) is always equal to 2π regardless oft he value of B B. The period of y=sin(Bx) is the length of the interval that results from the solution to the three-part inequality -2π ≤ Bx≤ 2π C. The period of y=sin(Bx) is the length of the interval that results from the solution to the three-part inequality 0 ≤ Bx≤ 2π D. The period of y=sin(Bx) is the length of the interval that results from the solution to the three-part inequality 0 ≤ Bx ≤ π
C
Which of the following statement 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 right C units B. The graph of y=sin (x+C) can be obtained by horizontally shifting each quarter point of y=sin(x) vertically down 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 left C units D. The graph of y=sin (x+C) can be obtained by horizontally shifting each quarter point of y=sin(x) vertically up C units
B
Which of the following statements is not true A. the period of y=sec x is P=2π B. The function y=sec x is obtains a local maximum at values of x for which the function y=cos x obtains a local maximum C. The range of y=sec x is identical to the range of y=csc x D. The domain of y=sec x {x|x≠(2n+1)π/2, where n is an integer}
D
Which of the following statements is true A. The function y=tan x is one-to-one B. The zeros of y=tan x are all values of x for which cos x=0 C. The domain of y=tan x is all real numbers except for values of x for which sin x=0 D. The x-intercepts of y=tan x are the same as the center points of y=tan x
B
Which of the following statements is true A. the domain of y=cot x is all real numbers except for values of x for which cos x=0 B. the function y=cot x has infinitely many vertical asymptotes with equations x=nπ where n is an integer C. The zeros of y=cot x are of the form nπ/2 where n is an integer D. The principle cycle of the graph of y=cot x occurs on the interval (-π/2, π/2)
B
If θ= tan^-1(x), then which of the following statements best describe angle θ A.The angle θ is an angle satisfying the inequality π/2 < θ < 3π/2 having a terminal side lying in Quadrant II, Quadrant III, on the positive y-axis, on the negative x-axis, or on the negative y-axis B. 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 C. 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 on the negative x-axis D. The angle θ is an angle satisfying the inequality π < θ < 2π having a terminal side lying in Quadrant III, Quadrant IV, on the positive x-axis, on the negative x-axis, or on the negative y-axis
D
If θ=sin^-1(x), then which of the following statements best describes angle θ? A. The angle θ is an angle satisfying the inequality π/2 ≤ θ ≤ 3π/2 having a terminal side lying in Quadrant II, Quadrant III, on the positive y-axis, on the negative x-axis, or on the negative y-axis B. The angle θ is an angle satisfying the inequality π ≤ θ ≤ 2π having a terminal side lying in Quadrant III, Quadrant IV, on the positive x-axis, on the negative x-axis, or on the negative y-axis C. 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 on the negative x-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
B
Which of the following expressions does not result in an angle having a terminal side that lies in Quadrant I A. sin^-1(sin 4π/5) B. sin^-1(sin 6π/5) C. tan^-1(tan 8π/7) D. cos^-1(cos(-π/5))