Chapter 11B: Trig Graphing Review Sheet Test Wednesday 05/17/2017 1. The terminal ray of an angle drawn in standard position on the unit circle that measures 30 has 3 1 coordinates of,. Based on this information, state the exact value of all 6 trig functions. 2 2 2. If an angle has a positive secant but a negative cosecant then it must terminate in which of the following quadrants? (1) I (3) III (2) II (4) IV 3. Which of the following represents the range of the function y x (1) 60 y 60 (3) 16 y 4 (2) 0 y 20 (4) 4 y 16 6sin 10? 4. Given the sinusoidal graph with coordinates shown below, what is the value of its amplitude? Midline? 5. A periodic function has an equation y x two consecutive relative maximums on this graph? (1) 10 (3) 8 10cos 8 2. What is the horizontal distance between any (2) 2 (4) 4
6. The graph shown below can be described using the equation. Identify A, B and C. 7. The voltage used by most households can be modeled by a sine function. The maximum voltage is 120 volts, and there are 60 cycles every second. Which equation best represents the value of the voltage as it flows through the electric wires, where t is time in seconds? 1) 3) 2) 4) 8. A sine function is graphed below. Determine and state the amplitude and period of this function. 9. Which of the following lines would the graph of y x (1) x 0 (3) y 20 (2) x (4) y 9 5sin 14 not intersect?
10. The path traveled by a roller coaster is modeled by the equation. What is the maximum altitude of the roller coaster? 11. A person riding a Ferris wheel at a local fair makes one complete trip around in 10 minutes. Their height can be modeled using a sine function of the form y Asin( Bt) C, where t is the amount of time the person has been traveling, in minutes. Which of the following must be the value of B? (1) 10 (3) 10 (2) 1 20 (4) 5 12. How many full cycles of the function appear in π radians? 13. What is the period of the function? 14. What is the period of the graph? 15. What is the period of the function? 16. The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function, where t represents time, in seconds. How many seconds does it take the pendulum to complete one full cycle? 1) 5 2) 6 3) 3 4) 10
17. The volume of water in a tank varies periodically. At t 0 it is at its maximum of 650 gallons and at t 5 it is at its minimum of 120 gallons. Which of the following functions would best model the volume of water in this tank as a function of time in hours? 2 (1) V 265cos t385 10 V 770sin 10t 385 (2) (3) V t 385cos 5 265 (4) V 265sin t770 10 18. The terminal ray of an angle drawn in standard position passes through the point.508,.862 on the unit circle. Which of the following is closest to the cotangent of this angle? (1) 0.589 (3) 1.697 (2) 1.291 (4) 2.883 19. If is an angle drawn in the standard position with its terminal ray landing in the fourth quadrant and csc 5 cos?, then what is the exact value of 20. For the angle it's known that cot 0 and lie? (1) I (3) III (2) II (4) IV sin 0. In which quadrant does the terminal ray of 3 21. For an angle A it is known that sin A and cos A 0. Determine the value of cota. Show how you 4 arrived at your answer.
22. Given the following circle (note that it is not the unit circle) with the angle marked, state the values of each of the following: (a) The radius of the circle (b) sin (c) cos (d) tan (e) sec (f) csc (g) cot 23. A portion of the unit circle is shown below. Based on this information, determine the value of sec150 in exact form. Explain in a sentence how you arrived at your answer. 30 24. The graph shown below can be modeled using the equation cos A, B, and C. Show how you arrived at your results. y A Bx C. Determine the values of
25. If the function y Asin xc 8 marked. is graphed below, answer the following questions about point D What is the numerical value of the x-coordinate of point D? Show how you arrived at your answer. D What is the y-coordinate of D in terms of the constants A and C? 26. A person's height, in feet above the ground, on a Ferris wheel can be modeled using the equation t ht 45cos 52, where t is the time the rider has been on the wheel in minutes. What is the 7 maximum height the rider reaches and the time it takes to first reach this height if they get on at t 0. Explain how you arrived at your answer.
27-30: Graph one period on either side of the y-axis for each function below without the use of your calculator. State the range of each graph 27. 28.
29. 30.
31 33 32
34 35 36