The values of the parameters of the sinusoidal function are [tex]A = 2[/tex], [tex]B = \frac{\pi}{3}[/tex] and [tex]H = 4[/tex], respectively.
According to this question, a sinusoidal function is described as following:
[tex]f(x) = \Delta y \cdot \sin \frac{2\pi\cdot x}{T} + y_{o}[/tex] (1)
Where:
By direct comparison, we have the following equivalencies:
[tex]A = \Delta y[/tex] (2)
[tex]B = \frac{2\pi}{T}[/tex] (3)
[tex]H = y_{o}[/tex] (4)
By (3) and [tex]T = 6[/tex], we have that:
[tex]B = \frac{2\pi}{6}[/tex]
[tex]B = \frac{\pi}{3}[/tex]
Then we find the remaining variables by using the following system:
[tex]2 = A \cdot \sin \left(\frac{3\pi}{2} \right) + H[/tex]
[tex]2 = -A + H[/tex] (5)
[tex]5 = A\cdot \sin \left[\left(\frac{\pi}{3} \right)\cdot (2.5)\right] + H[/tex]
[tex]5 = A\cdot \sin \frac{5\pi}{6} + H[/tex]
[tex]5 = \frac{1}{2}\cdot A + H[/tex] (6)
The solution of this system of equations is: [tex]A = 2[/tex], [tex]H = 4[/tex]
The values of the parameters of the sinusoidal function are [tex]A = 2[/tex], [tex]B = \frac{\pi}{3}[/tex] and [tex]H = 4[/tex], respectively.
To learn more on sinusoidal functions, we kindly invite to check this verified question: https://brainly.com/question/12078395
