Module 7 Test Review ~ Calculator



Module 7: Graphing Trig Functions Test Review ~ Calculator

1. A group of CHS students decided to students decided to study the sinusoidal nature of tides. Values for the depth of the water level were recorded at various times. At [pic] hours low tide was recorded at a depth of 1.8m. At [pic] hours, high tide was recorded at a depth of 3.6m

a. Write a function expressing distance in terms of time.

b. Sketch the graph of the function.

c. What was the depth of the water at [pic] [pic] [pic]

d. What are the first two times when the depth of the water is 2.5m?

2. One complete push-up takes 3 seconds. The student starts the push-up at 20 inches above the ground and finishes the push-up at 3 inches above the ground.

a. Write a function expressing distance in terms of time.

b. Sketch the graph of the function.

c. After how many seconds is the student 15.5 inches above the ground?

d. How far above the ground is he after 5.75 second?

3. The jack on a oil well goes up and down, pumping oil out of the ground. As it does so, the distance varies sinusoidally with time. At [pic], the distance is at its maximum, 3.7 meters. At [pic], the distance is at its minimum, 1.5 meters.

a. Write an equation.

b. Sketch the graph.

c. Find the distance when [pic].

d. Find the first time when the distance is 1.78 meters.

4. If the equilibrium point is [pic], then [pic] models a buoy bobbing up and down in the water.

a. Where is the buoy at [pic] [pic]

b. What is the maximum height of the buoy? The minimum?

c. What is the period?

5. A weight attached to the end of a long spring is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time. You start a stopwatch. When the watch reads 0.3 sec, the weight reaches a high point of 60 cm above the floor. The next low point, 40 cm above the floor, occurs at 1.8 sec.

a. Write the equation that expresses the motion of the spring over time.

b. Sketch the graph.

c. Predict the distance from the floor when the stopwatch reads 17.2 sec.

d. What was the distance from the floor when you started the stopwatch?

6. As the paddlewheel turned, a point on the paddle blade moved back in such a way that its distance, d, from the water's surface was a sinusoidal function of time. When a stopwatch read 4 seconds the point was at it's highest, 16ft about the water's surface. The wheel's diameter was 18 ft and it completed a revolution every 10 seconds.

a. Write the function that expresses the distance above the water’s surface in terms of time.

b. Sketch the function.

c. What was the distance of the point above the water’s surface after 5 sec? 35 sec?

d. What were the first three times when the point was at 9 ft above the water’s surface?

7. A ferris wheel is 50 ft in diameter, with the center 60 ft above the ground. You enter from a platform at the 3oclock position. It takes 80 sec to complete one revolution.

a. Find the equation that gives you your height when you entered the ferris wheel above the ground at t time. (t=0 when you entered).

b. Sketch the graph

c. After how many seconds were you 75 feet above the ground?

***** STUDY YOUR ALGEBRA REVIEWS #1 & #2 *****

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