Annalie T.

asked • 02/05/16

Finding alpha to model a sinusoidal wave

I am modelling a graph in the form y = Asin(ωt +α) +c, but I have got stuck on calculating alpha.
So far I have calculated...
  • the central line is at y=100
  • A = 24
  • period = 38
  • ω = 360/38 = 9.47368...
Apparently, α = -113.6842105
How do I get alpha to equal this number??! None of the methods I have tried give this answer.....or is the answer book just wrong!?

Elwyn D.

Why shouldn't α = -113.6842105?,  α is your phase angle.
A sine wave will go through the origin when ωt = 0, or actually in this case the point (0,100) since your curve is translated 100 units up.
Assuming you are working in degrees, this phase shift indicated means the graph will cross y = 100 at 113.6842105º when t = 0. 
I don't have the graph you are looking at, so I cannot justify any phase angle.  That part of your answer is logically independent from all the factors you have provided: Amplitude, period, and y-axis translation.  Phase shift corresponds to translation along the x-axis.


Elwyn D.

For some reason Wyzant did not post this comment at first.  My second post, seen below, has more information.


Annalie T.

Thanks you guys!!....I have really made sense of this now :)


2 Answers By Expert Tutors


Mark M. answered • 02/05/16

5.0 (243)

Mathematics Teacher - NCLB Highly Qualified

Mark M.

y = A(sinBx + C) + D
period = 2π/B, in this case B = π/19
phase shift = -C/B, this has three variables.
Since you do not know the phase shift determination of C is not possible.


Elwyn D. answered • 02/05/16

5.0 (58)

Private School Math Instructor

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