Question

A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days). Assume that the number of hours of daylight varies sinusoidal over a period of twelve months. Sketch a graph to model the hours of daylight and write a sine equation to model the hours of daylight using the information above and a phase shift of pi/2.

Answer 1

The equation is given as

$y = 12 sin (6t - \pi /2) + 2$

The Amplitude

The Amplitude can be calculated as

$amplitude = \frac{max + min}{2}\\ amplitude = \frac{10+14}{2} = 12$

The Vertical Shift

The vertical shift is the average difference between the maximum and minimum.

$Vertical Shift = \frac{Max - Min}{2} = \frac{14-10}{2} = 2$

For b value

The Time Period will be twice the distance between max and min.

$time period = \frac{2\pi }{b} \\time period = 2 * distance between max and min\\b = \frac{2\pi }{2}*\frac{1}{b} = \frac{\pi }{6}$

The Period

The period is calculated as

$T = \frac{2\pi }{b} \\T = \frac{2\pi }{\frac{\pi }{b} } = 12$

The equation is given as

$y = 12 sin (6t - \pi /2) + 2$

Learn more on time period and amplitude here;

brainly.com/question/15531840