More applications of trig functions and Pre-Test.

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.

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:
(b) What is the maximum depth of the water? When does it occur?

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:
(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.

6. 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.

7. Transformations
Pre-Test
Quowned By The Cal

13. (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.

14. (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.

15. (d) For how long, during each revolution, is the point A within 4 meters of
the water's surface?

16. 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

17. 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

18. 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

19. 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