Trig 7.1-7.5

If​ A, B, and C are constants such that B>1​, then which of the following statements is true about the graph of y=Acos(Bx−C)​?

The period is 2π/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=Acos(Bx−C)+D​?

The range is [−A+D, A+D]

Which of the following is NOT a characteristic of the sine function?

The sine function obtains a relative maximum at x=π/2+πn where n is an integer.

When sketching functions of the form y=Asin(Bx−C)+D and y=Acos(Bx−C)+D​, which of the following statements is​ true?

An interval for one complete cycle of the graph is where P is the period of the given function.

Which of the following statements is not true about the function y=Acos(Bx)​?

If B>0​,then the function y=Acos(−Bx) is equivalent to the function y=−Acos(Bx).

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 between the maximum and minimum values.

If θ=cos−1x​, then which of the following statements best describes angle θ​?

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.

If θ=tan−1x​, then which of the following statements best describes angle θ​?

The angle θ is an angle satisfying the inequality −π2<θ<π2 having a terminal side lying in Quadrant​ I, Quadrant​ IV, or on the positive​ x-axis.

If θ=sin−1x​, then which of the following statements best describes angle θ​?

The angle θ is an angle satisfying the inequality −π2≤θ≤π2 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.

Which is true?

The function y=cot x has infinitely many vertical asymptotes with equations x=nπwhere n is an integer.

Which is NOT true?

The function y=secx obtains a local maximum at values of x for which the function y=cosx obtains a local maximum.

Which is NOT true?

The graph of y=cscx is symmetric about the​ y-axis.

Which of the following statement best describes the graph of y=sin(x+C) where C>0​?

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.

When sketching the graph of y=Atan(Bx+C)+D which of the following 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 between the​ x-coordinate of the center point and a vertical asymptote.

Which is true?

The​ x-intercepts of y=tanx are the same as the​ x-coordinates of the center points of y=tanx.

What is the domain of the restricted cosine function whose inverse function is y=cos−1x​?

[0, pie]

Which of the following is not a characteristic of the cosine​ function?

the y-intercept is 0