The graph of a sinusoidal function intersects its midline at (0,2) and then has a minimum point at (3,-6) So, the function is f(x) = -8sin(pi/6x)+2.
What is the sinusoidal function?
The sinusoidal function has the following form:
[tex]y = x_0 + A\: sin(w.x+\theta)[/tex]
Where:
A= Amplitude
w = Angular frequency
[tex]x_0[/tex] = Independent component of the midpoint value
[tex]\theta[/tex] = Phase angle
Amplitude is the absolute value of the difference between a dependent component of the midline and the absolute minimum
A = |-6 - 2|
A = 8
[tex]x_0[/tex] = 2
The angular frequency of the function is now determined by substituting all remaining variables and clearing it within the sinusoidal function
[tex]w.x + \theta = \pi / 6[/tex]
The sinusoidal function
f(x) = -8sin(pi/6x)+2
Learn more about a sinusoidal function:
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