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8-23. Cooper Toy Company has designed a new toy that oscillates up and down and its position can be modeled by a sinusoidal curve. At time t = 5 seconds, the toy is at its maximum height, 18 cm above the ground. Four seconds later, the toy is at its minimum height, 6 cm above the ground. Write an equation to model the height, in centimeters of the toy at any time t, in seconds.

823 Cooper Toy Company has designed a new toy that oscillates up and down and its position can be modeled by a sinusoidal curve At time t 5 seconds the toy is a class=

Respuesta :

Given data:

The maximum height of the toy at t=5 seconds is M= 18 cm.

The minimum height of the toy at t=9 seconds is m=6 cm.

The expression for the amplitude is,

[tex]\begin{gathered} A=\frac{M-m}{2} \\ =\frac{18-6}{2} \\ =6 \end{gathered}[/tex]

The expression for the mean value is,

[tex]\begin{gathered} x=\frac{18+6}{2} \\ =12 \end{gathered}[/tex]

The period of the given curve is,

[tex]\begin{gathered} P=\frac{2\pi}{10} \\ =\frac{\pi}{5} \end{gathered}[/tex]

The equation for the given curve is,

[tex]y=6\cos (\frac{\pi}{5}(t-4))+12[/tex]

Thus, equation of the given curve is y=6 cos(π(t-4)/5)+12.

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