Annalie T.

# 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.

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02/05/16 Elwyn D.

For some reason Wyzant did not post this comment at first.  My second post, seen below, has more information.
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02/05/16

Annalie T.

Thanks you guys!!....I have really made sense of this now :)
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02/11/16

## 2 Answers By Expert Tutors

By: Tutor
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.
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02/05/16 Tutor
5.0 (58)

Private School Math Instructor

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