Question

write a sinusoid equation for the given situation and clearly explain how you determined the AMPLITUDE, VERTICAL and PHASE SHIFT.( the equation should have exact values no decimal of approximations. your equation should be in radians.)Centennial Colorado averages the maximum amount of daylight hours in June at 15 hours and the least amount in December at 9.4 hours. Assume that the number of hours of daylight varies sinusoidally over a period of 12 months. Develop a model for the number of hours of daylight as a function of time

Answer 1

y = A sinX

Maximum value= 15

Minimum value= 9.4

Amplitude= ( 15 - 9.4 )= 5.6/2 hours

Vertical shift = 15 - 2.8= 12.2 hours

Phase shift

June = 6th month

December= 12th month

X + delta

when x= 15 , sin ( 6 /12+ delta) = 1

and. x = 9.4 ,. Sin (12/12 + delta) + 2.8 = 0

then

Sin ( 6 /12 + delta) = 1

arcsin 1= 90°

Sin (12/12 + delta) = 2.8/12= 0.23

Then arcsin 0.23= 13.29 °

Then answer is

y = 15• Sin ( X + 0.5)