We want to get a point on the midline and the next maximum or minimum to that point, we will get: (0, 3) as a point on the midline, and (1/36, 9) as the next maximum to it.
A general sine function is written as:
f(x) = A*sin(w*x + p) + M
Where:
A is the amplitude.
w is the angular frequency.
M is the midline
p is the phase shift.
Here we know that:
Frequency = 18π = w
Amplitude = 6 = A
Midline; y = 3 = M
Then we have:
f(x) = 6*( 18π*x + p) + 3
We also know that when x = 0, the function is equal to 3, this implies that the sine has no phase shift, then p = 0, and the function is:
f(x) = 6*(18π*x) + 3
Now we need to get:
A point on the midline; (0, 3) is on the midline so we use that.
A second point must be a maximum or a minimum closest to the first point.
We know that the sine function has a maximum at sin(x = π/2)
Then we must solve:
18π*x = π/2
18*x = 1/2
x = 1/2*18 = 1/36
Then we have a maximum at: (1/36, 9)
Where the y-value of the maximum is just given by the midline plus the amplitude.
If you want to learn more, you can read:
https://brainly.com/question/21484188
