Question

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.​

Answer 1

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