f a Nocturnal Animal Many activities of living organisms are periodic. nocturnal

Question

f a Nocturnal Animal Many activities of living organisms are periodic. nocturnal Activity o For example, the graph at the right below shows the time that a certain animal begins its evening activity (a) Find the amplitude of this graph. (b) Find the period. Activity of a Nocturnal Animal 8:00 7:30 7:00 6:30 (c) Write the equation y=f(x) that represents the graph in the picture, where represents the month of January, yis the time of the day and y-0 represents 6:00 PM i 5:30Apr Jun Aug Oct Dec Fey Apr .ilfili:. 5:00 4:30 4:00 Month

Explanation / Answer

comparing with y=Asin(Bx +C) +D

minimum = 4, maximum = 8

(a)

amplitude ,A= (8-4)/2

amplitude ,A= 2

(b)

period =12

=>2/B =12

=>B=(/6)

D= (8+4)/2

=>D=6

c)

y=2sin((/6)x +C) +6

x=1 , represents january

=> x=3 represents march

y=0 at x =3

=>2sin((/6)*3 +C) +6 =0

=>2sin((/2) +C) =0

=>sin((/2) +C) =0

=>(/2) +C=0

=>C=-(/2)

equation is y=2sin((/6)x -(/2)) +6

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