the water depth in a harbour is 21 m at high tide and 11 m at low tide. one cycle is completed approximately every 12 h

Question

determine the equation (sine, cosine)

Answer 1

Hi Kevin

 

The general form for a sinusoid function is Asin(Bx + C) + D. A is the amplitude (half the vertical distance from the minimum to the maximum), B determines the period, C determines the horizontal shift, and D gives the vertical shift.

 

For this problem, the range is 10 meters (from 11 to 21). The amplitude is half the range, so A will be 5.

 

The period is 12 hours. For sine and cosine, period = 2π/B. If we set this equal to 12, we get B = π/6.

 

The problem doesn't specify when the high/low tide happens, so we can let C=0.

 

Finally, we need to vertically shift the function so the function is centered halfway between our desired high and low points. That center should be at y=16 (halfway between 11 and 21), so D=16.

 

So the function is: 5sin((π/6)x)+16. (You could also use cosine.)

 

Best

Julian