# Trig Questions Chp. 7

which of the following is not a characteristic of a sine function?

x=π/2+πn (because sine period is at 2π)

which is not a characteristic of cosine?

the y-intercept is at 0

which of the following statements describes the definition of amplitude of a sine or cosine function?

the amplitude is the measure of half the distance b/w the max + min values

if y=sin(bx) where b>0, then which of the following statements is true?

0<bx<2π

which of the following statements is not true about the function y= a cos (bx)?

y= a cos (-bx) is equal to y= - a cos (bx)

which best describes the graph y=sin(x+c) where c>0?

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

if a,b,c are constants such that b>1, then which of the following statements is true about the graph of cos?

the period is 2π/b and ps is c/b

if a,b,c, and d are constants, then which of the following is true about the graph of cos?

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

which of the functions of the form y=Asin(Bx-C) and y=Acos(Bx-C)+D is true?

an interval for one complete cycle of the graph is [C/B, C/B+P] where P is the period of the given function

which is true?

the x-intercepts of y=tan(x) are the same as the x-coordinates of the center points of y=tan(x)

which best describes how to determine the x-coordinates of the halfway points of the principal cycle?

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

what is true?

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

which is not true?

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

which is not true?

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

if θ=sin-1x, which best describes angle θ?

the angle θ is an angle satisfying the inequality -pi/2 < 0 < pi/2 having a terminal side in QI, QIV, the pos. x-axis, or neg. y-axis

if θ=cos-1(x)?

0<θ<pi

if tan-1(x)?

-pi/2<θ<3pi/2

domain of cos-1(x)?

[0,pi]

range of tan-1(x)?

(-pi/2,pi/2)

if 3pi/4<θ<5pi/6, which of the following mathematical statements is true?

cos-1(cosθ)=θ

which of the following is equivalent to the angle pi/6?

tan-1(tan(-5pi/6))

given the expression csc(cos-1(-1/2)), which of the following is not true?

the expression csc(cos-1(-1/2)) is equal to -2/√3