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

High = 5 = max

Low =1 = minimum

Average = 3

Amplitude = 5-3 = 2 = A

Midline = (5+1)/2 = 3 = D

Period = 2pi/B

B = 2pi/Period = 2pi/12 = pi/6

C = phase shift

f(t) = AcosB(t-C) + D

= 5cos[(pi/6)(t -C) + 3

calculate C so CosB(t-C) = +1

t-C = 0

12-C =0

C = 12

period is usually 12 hours for tides, two per 24 hour day

low tide is usually mid way between 2 high tides, which in this example would be 6pm not 4pm

4pm might be a mistake, miscopied or misprinted

if not, then the above formula for f(t) is Not correct