Use a cosine function to describe the height of the tides of the ocean if high tide raises the water level to 5 m at noon and low tide drops it down to 1 m at 4 p.m. Let t = 0 be 12 noon.

Question

Use a cosine function to describe the height of the tides of the ocean if high tide raises the water level to 5 m at noon and low tide drops it down to 1 m at 4 p.m. Let t = 0 be 12 noon.

Grade 12 Advanced Functions

Please write neatly and clearly. Thanks

Answer 1

Hi Math H.,

We can use h(t) = Acos[B(t - C)] + D, where A = amplitude; B = 2π/P (P= period); C = horizontal shift (phase shift); D = vertical shift.

For a tide with a high of 5m and a low of 1m, for a difference of 4m, produces an amplitude of A = 2, and a midline (vertical shift) of D = 3.

Since time t = 0 starts at noon at high tide, there is no phase shift C = 0.

It takes 4 hours for 1/2 a wave (high to low), therefore the whole wave takes 8 hours and P = 8.

And B = 2π/P = 2π/8 = π/4

∴ h(t) = 2*cos(π*t /4) + 3, graph on Desmos and have a look.

I hope this helps, Joe.