The graph of a sinusoidal function has a maximum point at (0,7) and then intersects its midline at (3,3). Write the formula of the function, where x is entered in radians. f(x)=

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The graph of a sinusoidal function has a maximum point at  (0,7) and then intersects its midline at  (3,3). Write the formula of the function, where  x is entered in radians.  f(x)=

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Given Points Information: We are given a maximum point at (0,7) and a midline intersection at (3,3). The maximum point gives us the amplitude and the vertical shift, while the midline intersection gives us the horizontal shift and the period.Calculate Amplitude: The amplitude (A) is the distance from the midline to the maximum point. Since the midline is at y = 3 and the maximum is at y = 7, the amplitude is 7 - 3 = 4.Calculate Vertical Shift: The vertical shift (D) is the y-value of the midline, which is 3.Determine Sinusoidal Function Form: The sinusoidal function will have the form f(x) = A * sin(B(x - C)) + D or f(x) = A * cos(B(x - C)) + D. Since the maximum point is at x = 0, we will use the cosine function, which has a maximum at x = 0 when there is no horizontal shift (C = 0).Find Period of Function: Now we need to find the period (T) of the function. The graph intersects the midline at (3,3), which is a quarter of the period after the maximum. Therefore, the full period is 4 times this value, so T = 4 * 3 = 12 radians.Calculate B Value: The value B in the function f(x) = A * cos(B(x - C)) + D is related to the period by the formula B = 2π / T. So B = 2π / 12 = π / 6.Final Sinusoidal Function: Putting all the values together, we get the sinusoidal function: f(x) = 4 * cos(π/6 * (x - 0)) + 3.

The graph of a sinusoidal function has a maximum point at $(0,7)$ and then intersects its midline at $(3,3)$ . $\newline$ Write the formula of the function, where $x$ is entered in radians. $\newline$ $f(x)=$

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The graph of a sinusoidal function has a maximum point at (0,7)(0,7)(0,7) and then intersects its midline at (3,3)(3,3)(3,3).\newlineWrite the formula of the function, where xxx is entered in radians.\newlinef(x)=f(x)=f(x)=

The graph of a sinusoidal function has a maximum point at $(0,7)$ and then intersects its midline at $(3,3)$ . $\newline$ Write the formula of the function, where $x$ is entered in radians. $\newline$ $f(x)=$