Question

Please help! In a tidal river, the time between high and low tide is 5.8 hours. At high tide, the depth of water is 17.2 feet, while at low tide the depth is 4.6 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine).

Write an equation for the depth () of the tide (in feet) hours after 12:00 noon.

Answer 1

Explanation:

mean tide is (17.2 + 4.6)/ 2 = 10.9 ft

Amplitude of tide is (17.2 - 4.6)/ 2 = 6.3 ft

The full tide cycle is 2(5.8) = 11.6 hrs

As we are not told the tide condition at 12:00 noon,

I will ASSUME that the tide is high and use the cosine function

D = 10.9 + 6.3cos(2π(t/11.6)) ft

where t is in hours after noon high tide.

make sure your calculator is set to radians.

If you want to use degrees, the equation becomes

D = 10.9 + 6.3cos(360(t/11.6)) ft