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# Pre-Cal 40S Slides March 12, 2008

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More applications of trig functions and Pre-Test.

More applications of trig functions and Pre-Test.

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• 1. The Mathematics of Tidal Waves Giant waves on the seafront at Seaham, County Durham by freefotouk
• 2. At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula: (a) State the: (i) period (ii) amplitude (iii) phase shift.
• 3. At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula: (b) What is the maximum depth of the water? When does it occur?
• 4. At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula: (c) Determine the depth of the water at 5:00 am and at 12:00 noon. (d) Determine one time when the water is 2.25 meters deep.
• 5. At a sea port, the depth of the water, h meters, at time, t hours, during a certain day is given by this formula: (d) Determine one time when the water is 2.25 meters deep.
• 6. Transformations Pre-Test Quowned By The Cal
• 7. (b) Write a sine and a cosine equation for this function. (c) Find one time when the point A is 4 meters above the water.
• 8. (b) Write a sine and a cosine equation for this function. (c) Find one time when the point A is 4 meters above the water.
• 9. (d) For how long, during each revolution, is the point A within 4 meters of the water's surface?
• 10. A Ferris whell has a radius of 20 m. It rotates once every 40 seceonds. Passengers get on at point S, which is 1 m above ground level. Suppose you get on at S and the wheel starts to rotate. (a) Graph how your height above the ground varies during the first two cycles. (b) Write an equation that expresses your height as a function of the elapsed time. (c) Determine your height above the ground after 45 seconds. (d) Determine one time when your height is 35 m above the ground. JAMIE ELVEN KRISTINA
• 11. This equation gives the depth of the water, h meters, at an ocean port at any time, t hours, during a certain day. (a) Explain the significance of each number in the equation: (i) 2.5 (ii) 12.4 (iii) 1.5 (iv) 4.3 (b) What is the minimum depth of the water? When does it occur? (c) Determine the depth of the water at 9:30 am. (d) Determine one time when the water is 4.0 meters deep. PAUL NELSA LAWRENCE
• 12. On a typical day at an ocean port, the water has a maximum depth of 20 m at 8:00 am. The minimum depth of 8 m occurs 6.2 hours later. Assume that the relation between the depth of the water and time is a sinusoidal function. (a) What is the period of the function? (b) Write an equation for the depth of the water at any time, t hours. (c) Determine the depth of the water at 10:00 am. (d) Determine one time when the water is 10 m deep. THI JUSTICE JOSEPH FRANCIS
• 13. Tidal forces are greatest when Earth, the sun, and the moon are in line. When this occurs at the Annapolis Tidal Generating Station, the water has a maximum depth of 9.6 m at 4:30 am and a minimum depth of 0.4 m 6.2 hours later. (a) Write an equation for the depth of the water at any time, t hours. (b) Determine the depth of the water at 2:46 pm. (b) How long is the water 2 meters deep or more during each period. BEN JOYCE RICHARD ROXANNE