Sine Graph for Tidal Waves

[speedli795]

We were given a problem on a recent test that asked us to find a function for a Sinusoidal Tidal Wave. I made my y-axis symbolize 8 A.M. and found the function:

. . .Y = 3sin(0.523(x - 12)) + 4

However, most other students (as well as the teacher) started the graph at 12 P.M. (four hours later) and found the function:

. . .Y = 3sin(0.523(x - 8)) + 4

Are these identical equations, and is either one correct? Do I have a case to claim my equation is just as correct?

In addition, is there generally only one correct answer for such a problem (proving my method to be incorrect)?

Thanks for the time and I appreciate the help.

 

[stapel]

From what you learned back in algebra about functions, you know that f(x + 4) is the same as f(x), but shifted four units to the left. So sin(x - 8) is the same as sin(x - 12), but shifted four units to the left.

In other words, as long as you define what "x = 0" stands for, the two functions should measure the same thing.

Also note that, since cos(x) = sin(x + pi/2), then any sine curve could be turned into an equally-valid cosine curve. Obviously, this means that there are at least two "right" (mathematically valid) answers to any "sinusoidal curve" problem.

Eliz.