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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.

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.

  • Math -

    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)

  • Math -

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

  • Math -

    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.

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