Question

The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (0.75,7).

Answer 1

Answer: y(x) = 2*sin(4.19*x) + 5

Step-by-step explanation:

We know that the midline is at x = 0 and y = 5, and the maximum is at x = 0.75 and y = 7

The midline of a graph is a horizontal line that cuts our graph in the middle.

For a normal cosine or sine function, the middle value is zero, so the middle line would be at y = 0, but here we have the midline at (0, 5) so it is located at y = 5.

This means that we have a constant in our function, so it is:

y(x) = f(x) + 5

where f(x) is a trigonometric function.

y(0) = 5 = f(0) + 5

so f(0) = 0

Now we know that sin(0) = 0

Then we have that f(x) = A*Sin(c*x) where A and c are constants.

Now, the maximum of our function is at x = 0.75

and we know that the maximum of the sin(x) is at x = pi = 3.14

then we have:

c*0.75 = 3.14

c = 3.14/0.75 = 4.19

and we have that:

f(0.75) = 7 = A*sin(4.19*0.75) + 5 = A + 5

A + 5 = 7

A = 7 - 5 = 2

Then our function is:

y(x) = 2*sin(4.19*x) + 5