posted by Axel on .
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.
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)
how can i put that in the form of A cos B (t- C)+D and A sin B (t- C)+D?
surely you can see that
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.