Alg 2 BC U11 Day 6 – Modeling with Sine and Cosine
1. Suppose the waterwheel below rotates at 6 revolutions per minute (rpm). The diameter of the wheel is 7 feet, of which 1 foot is below the level of the water. You choose a point P on the rim of the wheel and start your stopwatch. Two seconds later, point P is at its greatest height.
Write a sine equation to model the distance d of point P from the surface of the water in terms of the number of seconds t the stopwatch reads.
** You will need to find the values of a, b, c and d. That means you will need to determine:
Amplitude:
Period:
Phase Shift:
Vertical Translation:
2. As you ride a Ferris wheel, your distance varies with time. After waiting until all of the riders have loaded, the ferris wheel finally starts rotating. Let t be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes you 3 seconds to reach the top, 43 feet above the ground, and that the wheel makes a revolution once every 8 seconds. The diameter of the wheel is 40 feet. Find a SINE and a COSINE equation to model your height above ground as a function of time since the ferris wheel started.
3. A theme park is building a portion of a roller coaster track in the shape of a sinusoid.
The high and low points of the track are separated by 50 meters horizontally and 30 meters vertically.
The low point is 3 meters below the ground. Let y be the distance above the ground of the track (in meters) at any particular point. Let x be the horizontal distance (in meters) a point on the track is from the high point. Sketch a
graph and find a particular equation for y as a function of x.
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 mathematically model his motion and starts her stopwatch. Let y be the number of feet Tarzan is (horizontally) from the river bank. Assume that y is positive when Tarzan is over water and negative when he is over land. Jane finds that when t = 3, Tarzan is at one end of his swing, over land, 20 feet from the river bank. When t = 7, he reaches the other end of the swing, over the water, 14 feet from the river bank. Sketch a graph and write and equation for this function.
5. Below is a chart showing the monthly average high temperatures in Philadelphia. Write an equation to model the date. Be sure to state what each of your variables represents.