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# Pre-Cal 40S March 13, 2009

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Pi Day 2009 ... approximately.

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### Pre-Cal 40S March 13, 2009

1. 1. π Happy (approximation) Day! Pi sculpture by ﬂickr user niallkennedy
2. 2. The Reciprocal Trigonometric Functions ...
3. 3. sketch the graph of Given
4. 4. The Reciprocal Trigonometric Functions ...
5. 5. Graphing a quot;piece-wisequot; function ...
6. 6. Determine if the function ƒ(x) = |x| - x2 is even, odd, or neither.
7. 7. 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.
8. 8. 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.
9. 9. 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.
10. 10. 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.