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| PAGE: 426 | SET: Exercises | PROBLEM: 35 |
(a)
The number of hours of sunlight on the summer solstice of 
was 
.
The number of hours of sunlight on the winter solstice was 
.
Find the sinusoidal function of the form 
.
Where 
is amplitude and period is 
and phaseshift is 
.
The amplitude of the function is 
.
.
The amplitude of the function is 
.
The verticalshift of the fucntion is 
.
The verticalshift of the function is 
.
The days repeats every 
days, hence the time period for one cycle is 
.
Therefore, 
.
To find the horizontal shift , divide the time period 
days into four subintervals of length 
.
Hence the subintervals are 
.
The function of the sine wave is increasing on the interval 
and decreasing on the interval 
.
Hence a local maximum occurs at 
days.
But the maximum value of summer solstice occurs at 
days.
Therefore, the horizontal shift is 
.
hence 
.
Substitute , , 
, 
in 
.
.
Therefore, the sinusoidal function is 
.
(b)
Find the number of hours of daylight on April 
, the 
st day of the year.
Substitute 
in .
The number of hours to predict the daylight on April 
are 
.
(c)
Graph:
Graph the function .
.gif)
(d)
Graph:
Graph the function .
.gif)
Observe the graph :
The actual number of hours of daylight on April are 
is same as the predicted amount.
(a) The sinusoidal function is .
(b) The number of hours to predict the daylight on April are .
(c)
Graph of the function is
(d)
Observe the graph :
The actual number of hours of daylight on April are is same as the predicted amount.
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