Trigonometry Problem and Periodic Functions

Question

Tides can be modeled by periodic functions. Suppose high tide at the city dock occurs at 2 A.M at a depth of 38 meters and low tide occurs at 9 A.M at a depth of 18 meters.

A) Graph one cycle then write an equation that models the depth of the wave as a function of time after midnight.

B) When will the next high and low tides occur

Answer 1

If you consider time = 0 to be midnight, then a periodic formula will be of the form

Tide = 10cos(pi*t/7- 2*pi/7) + 28

at (t=2) 2am, Tide = 38,

at (t=9) 9am, Tide = 18

at (t=16) 4pm, Tide = 38

at (t=23), 11pm, Tide = 18