The equation is given as
[tex]y = 12 sin (6t - \pi /2) + 2[/tex]
The Amplitude can be calculated as
[tex]amplitude = \frac{max + min}{2}\\ amplitude = \frac{10+14}{2} = 12[/tex]
The vertical shift is the average difference between the maximum and minimum.
[tex]Vertical Shift = \frac{Max - Min}{2} = \frac{14-10}{2} = 2[/tex]
For b value
The Time Period will be twice the distance between max and min.
[tex]time period = \frac{2\pi }{b} \\time period = 2 * distance between max and min\\b = \frac{2\pi }{2}*\frac{1}{b} = \frac{\pi }{6}[/tex]
The period is calculated as
[tex]T = \frac{2\pi }{b} \\T = \frac{2\pi }{\frac{\pi }{b} } = 12[/tex]
The equation is given as
[tex]y = 12 sin (6t - \pi /2) + 2[/tex]
Learn more on time period and amplitude here;
https://brainly.com/question/15531840
