sinusoidal function
DESCRIPTION
Sinusoidal Function. A function with a graph that resembles a sine or cosine curve in the form of:. Big & little: the largest & smallest pieces of the given data. Where:. Solve for k:. Calculate c by substituting one set of ordered pairs after replacing A, k, & h. Calculate the total hours:. - PowerPoint PPT PresentationTRANSCRIPT
Sinusoidal Function
A function with a graph that resembles a sine or cosine curve in the form of:
hckay
hckay
)cos(
)sin(
Where:
2
littlebiga
2
littlebigh
kperiod
2Solve for k:
Calculate c by substituting one set of ordered pairs after replacing A, k, & h.
Big & little: the largest & smallest pieces of the given data.
14.12)sin(61.1
)sin(
6 cty
hcktAy
Next, choose an ordered pair from the data, plug into the equation & solve for c.
10.68 hrs
10.7 hrs
11.98 hrs
12.77 hrs
13.42 hrs
13.75 hrs
13.6 hrs
13.05 hrs
12.3 hrs
11.56 hrs
11.12 hrs
10.53 hrs
a = big minus little, div by 2
h = big plus little div by 2
Period is 12 months (from the data)
Calculate the total hours:
14.12)1sin(61.168.10 6 c
January: t = 1, y = 10.68
)sin(61.146.1 6 c
)sin( 661.146.1 c
161 sin)sin(9068.0sin c
c 61357.1
c
c
6593.1
1357.1 6
14.12)66.1sin(61.1 6 ty
The sinusoidal function representing the data is:
Do the math:
A = Dif of most/least div by 2
h = Sum of most/least div by 2
hcktAy )cos(
45.0)sin(37.0
)cos(
2 cty
hcktAy
t = 0, y = 0.08
c
c
c
c
c
0
coscos1cos
cos1
cos37.037.0
45.0))0(cos(37.008.0
11
2
(A must be negative, since at t=o the value is a minimum, the the graph goes up from there)
However, the phase shift will be different. To avoid a greater phase shift than necessary, use the following rule:
If the value of the function is about zero at x = 0, use sine
If the value of the function is a maximum or minimum at x = 0, use cosine.
The period is 4 seconds
HW: Page 391