MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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

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