Final answer:
To find the formula of the sinusoidal function, we need to determine the value of k. However, there is no solution for the equation sin(ρ) = 7/2, so we cannot determine the value of k and write the formula of the function.
Step-by-step explanation:
To find the formula of the sinusoidal function, we can use the general form:
y(x) = A sin(kx - ρ)
From the given information, we know that the midline intersects at (0, -7), so the midline equation is y = -7. The minimum point is at (pi/4, -9), which is below the midline by 2 units. This means the amplitude is 2 units.
Substituting these values into the general form, we have:
y(x) = 2 sin(kx - ρ) - 7
Now, we need to determine the value of k. Since the period of a sine function is 2π/k, we can use the fact that the midline intersects at (0, -7). This means when x = 2π/k, y should be -7.
Plugging in these values, we have:
-7 = 2 sin(k * (2π/k) - ρ) - 7
0 = 2 sin(2π - ρ) - 7
0 = 2 sin(-ρ) - 7
0 = 2 sin(-ρ) - 7
sin(-ρ) = 7/2
Since sin(-ρ) = sin(ρ), we have:
sin(ρ) = 7/2
Since the sine function oscillates between -1 and 1, there is no solution to this equation. Therefore, we cannot determine the value of k. Without the value of k, we cannot write the formula of the sinusoidal function.