The graph of a sinusoidal function has a maximum point at (0,8) and then has a minimum point at (5,2). 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  (0,8) and then has a minimum point at  (5,2). Write the formula of the function, where  x is entered in radians.  f(x)=____

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Calculate Amplitude:  Determine the amplitude of the sinusoidal function. The amplitude is half the distance between the maximum and minimum values of the function. Here, the maximum value is 8 and the minimum value is 2. So, the amplitude A is calculated as: A = (8 - 2) / 2 = 3. Identify Vertical Shift:  Identify the vertical shift of the function. The vertical shift is the average of the maximum and minimum values. Calculate it as: Vertical shift = (8 + 2) / 2 = 5. Calculate Period:  Calculate the period of the function. Since the function goes from a maximum at x = 0 to the next minimum at x = 5, half the period is 5. Therefore, the full period T is: T = 5 * 2 = 10. Determine Horizontal Shift:  Determine the horizontal shift (phase shift) of the function. Since the maximum occurs at x = 0, there is no horizontal shift. Thus, the phase shift c is 0. Write Sinusoidal Function Formula:  Write the formula of the sinusoidal function using the values calculated. The general form of a sinusoidal function is: f(x) = A * sin(B(x - C)) + D Where A is the amplitude, B is the frequency (B = 2π/T), C is the phase shift, and D is the vertical shift. Plugging in the values: f(x) = 3 * sin((2π/10)(x - 0)) + 5 Simplify B: f(x) = 3 * sin(π/5 * x) + 5.

The graph of a sinusoidal function has a maximum point at $(0,8)$ and then has a minimum point at $(5,2)$ . $\newline$ 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 (0,8) (0,8) (0,8) and then has a minimum point at (5,2) (5,2) (5,2).\newlineWrite the formula of the function, where x x x is entered in radians.\newline f(x)=_____

The graph of a sinusoidal function has a maximum point at $(0,8)$ and then has a minimum point at $(5,2)$ . $\newline$ Write the formula of the function, where $x$ is entered in radians. $\newline$ f(x)=_____