Name: Which equation is represented in the graph? Which equation is represented by the graph? 1. y = 2 sin 2x 2. y = sin x. 1.

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1 Name: Print Close Which equation is represented in the graph? Which equation is represented by the graph? y = 2 sin 2x y = sin x y = 2 sin x 4. y = sin 2x Which equation is represented in the graph? 4. y = 2 sin x y = sin 2x y = sin 2x 4. y = 2 sin x What is the period of the graph of the equation y = a sin bx? y = 2 cos 2x y = cos 2x y = 2 cos x 4. y = cos x a 4. b Page 1 of 10

2 5. The graph of which function has an amplitude of 2 and a period of 4π? 6. y = 2 sin x y = 2 sin 4x y = 4 sin x 4. y = 4 sin 2x What is the period of the graph of the equation y = 3 cos 4x? 8. What is the maximum value for the function y = sin 5x? Which of the statements below are true about the graph of y = cos θ? I. Domain: all real numbers II. Range: 1 y 1 III. Period: 2π I, only III, only II, only 4. I, II, and III The amplitude of the graph of the equation y = 3 sin 6x is 2π Page 2 of 10

3 10. 1 A student attaches one end of a rope to a wall at a fixed point 3 feet above the ground, as shown in the accompanying diagram, and moves the other end of the rope up and down, producing a wave described by the equation y = a sin bx + c. The range of the rope s height above the ground is between 1 and 5 feet. The period of the wave is 4π. Write the equation that represents this wave. The times of average monthly sunrise, as shown in the accompanying diagram, over the course of a 12- month interval can be modeled by the equation y = A cos (Bx) + D. Answer: y = sin x + Determine the values of A, B, and D. Answer: A =, B =, D = 1 If f(x) = 2 sin3x + C, where C > 0, then the maximum value of f(x) is: C C + 3 C C + 6 Page 3 of 10

1 The shaded portion of the accompanying map indicates areas of night, and the unshaded portion indicates areas of daylight at a particular moment in time. 15.

4 1 The shaded portion of the accompanying map indicates areas of night, and the unshaded portion indicates areas of daylight at a particular moment in time. 15. An object that weighs 2 pounds is suspended in a liquid. When the object is depressed 3 feet from its equilibrium point, it will oscillate according to the formula x = 3 cos (8t), where t is the number of seconds after the object is released. How many seconds are in the period of oscillation? Which type of function best represents the curve that divides the area of night from the area of daylight? quadratic tangent cosine 4. logarithmic 16. π π In physics class, Eva noticed the pattern shown in the accompanying diagram on an oscilloscope. 14. The path traveled by a roller coaster is modeled by the equation y = 27 sin 13x What is the maximum altitude of the roller coaster? y = sin x + 1 y = 2 sin x Page 4 of 10

5 17. Which equation is represented by the accompanying graph? 19. What is the phase shift of the following equation? π units to the right 1 unit up π units to the left 4. π units up 20. y = cos x y = cos x y = cos 2x 4. y = cos x 18. What is the phase shift of the following equation? What is the phase shift of the following equation? 2 3 units to the right 3 units to the left unit to the right 4. unit to the left If the period of a sine function is, what is the 10 units to the right 2 units up 10 units to the left units up frequency of the function? π 2 4. Page 5 of 10

6 2 What is the period of the following equation? 1 π π 2 What is the period of the following equation? 9 4. π Page 6 of 10

7 24. What is the equation of the graph below? y = cot(x) y = arctan(x) y = sin(x) 4. y = tan(x) Page 7 of 10

8 25. Which graph represents one complete cycle of the equation y = sin 3πx? 4. Page 8 of 10

9 26. Which equation is graphed in the diagram below? 27. Which function is represented in the accompanying graph over the interval π x π? 4. y = sin x y = cos x y = sin x 4. y = cos x Page 9 of 10

10 Answer Key for Exam 41 Review or -2, 1/2 or 0.5, , 0.5, Page 10 of 10

Graphing Sine and Cosine

Graphing Sine and Cosine The problem with average monthly temperatures on the preview worksheet is an example of a periodic function. Periodic functions are defined on p.254 Periodic functions repeat themselves each period. The