The water level (y) in a tank oscillates between 4 feet and 10 feet. It takes 20 seconds for the water level to go from 4 feet to 10 feet and seconds to go from 10 feet to 4 feet. At time(t)=0 seconds, the water level (y) is 10 feet.

Question

1. Write the equation for the depth in the form of y=A cos B (t- C)+D, where t=time in seconds and y=depth in feet.

2. Write the equation for the depth in the form of y=A sin B (t- C)+D, where t=time in seconds and y=depth in feet.

Answer 1

since y is a max when t=0, we want a cosine function, since cos(0) = 1.

y = 7+3cos(pi/20 t)

because the period is 40 seconds, and the level varies between 7+3 and 7-3 feet..

C=0 because cosine is a max at t=0, so there is no offset.

Naturally, you can now write the sine function, since cos(x) = sin(pi/2 - x)

Answer 2

how can i put that in the form of A cos B (t- C)+D and A sin B (t- C)+D?

Answer 3

surely you can see that
A=3
B=pi/20
C=0
D=7

I mean, just read it off.

Now employ your skills to convert your cos(x) to sin(pi/2-x)

A and D stay the same.