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.
