Trigonometry

Graphing Trig Functions

2020 June(C02) Math Question 17

The function y = 2 sin(6πx) is graphed in the standard (x,y) coordinate plane for x radians in the interval 0 ≤ x ≤ 1. What are the period and amplitude of the function?

2025 October(J08) Math Question 17

20. The graph • of y = 3 — 5 sin(x — n) is shown in the standard (x ,y) coordinate plane below. What is the range of y ?

2017 June(74C) Math Question 20

2011 June(69F) Math Question 28

2020 July(C01) Math Question 33

34. For an angle with measure a in a right triangle, sin a = 180/181 and tan a = 180/19. What is the value of cos a?

2015 April(73G) Math Question 34

2013 April(71G) Math Question 36

38. The function f(x) = 0.25 sin(4x) is graghed below for 0 <= x

2016 April(73E) Math Question 38

39. What is the amplitude of the function f(x) = 1/2 cos(3x + pi)?

2015 June(73C) Math Question 39

42. For all x such that 0 x < 90, which of the following . expressions is NOT equal to sin x° ?

2017 June(74C) Math Question 42

42. Suspended from the ceiling is a weight on a large spring that is oscillating up and down. The distance, d inches, between the location of the center of the mass of the weight after t seconds and the weight’s equilibrium location at t = 0 is modeled by the function d= 5 sin(4itt). What is the amplitude of the function?

2016 December(74H) Math Question 42

44. What is the amplitude of the function y = 3 sinx ?

Amplitude, Period, Phase Shift and Frequency

2021 December(E23) Math Question 44

2011 April(67F) Math Question 45

2018 December(B05) Math Question 48

49. The graph of y = a sin bx is shown below for certain positive values of a and b. One of the following values is equal to a. Which one?

2013 June(71C) Math Question 49

51. What are the values of 0, between 0 and 2pi, when tan 0 = —1 ?

2015 April(73G) Math Question 51

2009 April(66F) Math Question 53

55. The graph of y = sin x in the standard (x,y) coordinate plane is reflected over the x-axis, shifted up a units, and then shifted left 0.5pi units. Which of the following equations represents the graph after the 3 transformations?

2015 December(72E) Math Question 55

55. What is the period of the function f(x) = esc(4x) ?

2017 April(74F) Math Question 55

56. The functions y = sin x and y = sin(x + a) + b, for constants a and b, are graphed in the standard (x,y) coordinate plane below. The functions have the same maximum value. One of the following statements about the values of a and b is true. Which statement is it?

2014 June(72C) Math Question 56

57. Given that 2 sin a = 2 and 2 cos(- b) = 2, which of the following could be a value, in radians, of a + b ?

2014 December(72G) Math Question 57

57. Given that sin A = 5/13 and 0° A < 360°, what are all possible values of cos A ?

2014 April(71H) Math Question 57

2013 December(71E) Math Question 58

58. A cosine function is shown in the standard (x,y) coordinate plane below. One of the following equations represents this function. Which one?

Graphs of Sine, Cosine and Tangent

2021 April(Z04) Math Question 58

59. Consider the family of functions y = f(x)= sin x + c, where c is a real number. Which of the following number lines represents the graph of all and only the possible values of c for which the graph of y has no x-intercepts?

2018 June(A11) Math Question 59

59. For 5 0 5 1, ‘sin 01 1 is true for all and only the values of B in which of the following sets?

Graphing Trig FunctionsTrigonometryACT math questions

2020 June(C02) Math Question 17

2025 October(J08) Math Question 17