Pi Day 2009 ... approximately.

1. π
Happy
(approximation)
Day!
Pi sculpture by flickr user niallkennedy

2. The Reciprocal Trigonometric Functions ...

3. sketch the graph of
Given

4. The Reciprocal Trigonometric Functions ...

5. Graphing a quot;piece-wisequot; function ...

6. Determine if the function ƒ(x) = |x| - x2 is even, odd, or neither.

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. 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. 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. 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.