Question

You are shipwrecked on a tropical island and you built yourself a hut at the edge of the beach. At high tide the waterline is 10feet from your hut. At low tide the waterline is 30 feet from your hut. The time between high tides is 12 hours. Find the trigonometric equation that gives the distance the waterline is from your hut as function of of time in hours. Assume time zero is at high tide.

Answer 1

let our trigonometric function is a sine function

which is in the form of

.................(1)

.

The time between high tides is 12 so the periodicity of the function is T=12

periodicity is given by

.

At high tide, the waterline is 10feet from your hut. At low tide, the waterline is 30 feet from your hut.

the difference is

.

amplitude is

.

put all values in equation 1

...................(2)

we have assumed that time zero is at high tide.

so y(0)=10 feet

.................put in equation 2

.