Precalculus Honors Name_______________________

8.1-8.3 Quiz Review Date________________________

1. Determine the equation of the graph.

2. Graph 212

cos7

xy

. Show 2 full periods and label a high point, low point, and a

point on the sinusoidal axis.

Precalculus Honors Name_______________________

8.1-8.3 Quiz Review Date________________________

3. Solve x3sin23 in the domain 2,0 . Answers must be exact.

4. Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across

the river bank, going alternately over land and water. Jane decides to model mathematically his

motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and let y be

the number of meters Tarzan is from the river bank. Assume that y varies sinusoidally with t and

that y is positive when Tarzan is over water and negative when he is over land. Jane finds that

when t = 2, Tarzan is at one end of his swing where y = - 23. She finds that when t = 5 he

reaches the other end of his swing and y = 17.

a) Sketch a graph of this sinusoidal function.

b) Write an equation expressing Tarzan’s distance from the river bank in terms of t.

c) Predict y when: t = 2.8, t = 6.3, and t = 15.

d) Where was Tarzan when Jane started the stopwatch?

Precalculus Honors Name_______________________

8.1-8.3 Quiz Review Date________________________

5. True or False: The amplitude of a cosine function is the difference between its maximum and

minimum values.

6. True or False: The graph of any sine function can be described by an appropriately designed

cosine function.

Solve for 0,2 . Give solutions in terms of .

7. 2 cos 1 0x 8. 2sec 4x

10. For the given graph, find the amplitude, period, and equation of the curve.

11. Sketch 4 2cos3y x .

12. In San Francisco, the average height if the tide in feet t hours after high tide is given by the function

2

2 2cos12.4

h x t

. What is the smallest positive value of t corresponding to low tide? Sketch the

graph.