Designer functions Design a sine function with the given properties. NKS It has a period o

fortdefruitI 2021-08-16 Answered
Designer functions Design a sine function with the given properties. NKS It has a period of 12 hr with a minimum value of 4 at t=0 hr and a maximum value of 4 at t=6 hr.
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Expert Answer

Nathaniel Kramer
Answered 2021-08-17 Author has 78 answers

Step 1
Find the sine function satisying the properties.
The sine function: f(x)=Asin(2πp(xd))+c has amplitude A, A=f1f22 with the period p hr, d is the horizontal shift and c is the vertical shift. If d>0 graph shifts towards right and if d<0 graph shifts towards left, d=t1+t22. If c>0 graph shifts upward and if c<0 graph shifts downward, c=f1+f22.
Here f1 and f2 are the maximum and minimum value of function respectively, t1 and t2 are the points where function attains maximum and minimum value respectively.
Sine function with period of 12 hr with minimum value of 10 at t=3hr and maximum value of 16 at t=15hr.
We have p=12, f1=4, f2=4, t1=3 and t2=9
Step 2
Calculate A, d and c.
A=4(4)2
=4
d=3+92
=6
and
c=442
=0
Substitute the values in the function:
f(x)=4sin(2π12(x6))+0
=4sin(π6(x6))

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