The table shows the height, in feet, of the tide over time, in hours.
I know the answer is that it should be cosine instead of sine, but I don't how to determine that. I'd like to know so I could solve questions like these in the future.
For this case we have the following function: f (x) = - 4sine ((pi / 6) x) + 5 We evaluate the function for x = 0 f (0) = - 4sine ((pi / 6) 0) + 5 f (0) = -4 * (0) + 5 f (0) = 5 We note that the result does not correspond to the table. Let's rewrite the function: f (x) = - 4cosine ((pi / 6) x) + 5 We evaluate the function for x = 0 f (0) = - 4cosine ((pi / 6) 0) + 5 f (0) = -4 * (1) + 5 f (0) = 1 The result corresponds to the table Answer: The student's mistake is to use the sine function instead of using the cosine function. The correct function is: f (x) = - 4cosine ((pi / 6) x) + 5
