Troubleshooting a Singular Matrix When Modeling a Curve

[Peter G.]

When I try and model a curve using a sine regression with my graphic calculator, it returns an error message that says: Singular Matrix

I decided then to do it by hand. Here are three points.

Minimum: (0,554.8), Maximum: (45, 1220.5) and a random point (20, 830.7)

I want something in the format of: A*sin B(x-c) + d

This is what I did, is it correct?

A = (1220.5-554.8)/2
B = (2*pi)/45
D = (1220.5+554.8)/2
C = One unknown, so I used the random point shown to solve:

(Should I have calc in radians or degrees?)

My steps: ( I will use letters for simplicity)

830.7 = A*sinB(x-c)+d
830.7 - D = A*sinB(x-c)
Ans/A = sinB(x-c)
sin^-1(Ans/A) = B(x-c)
Ans/B=x-c
-c=(Ans/B)-x

But I am not getting anything sensible...

Is my calculator right or did I do anything wrong?

Thanks

 

[HallsofIvy]

When I try and model a curve using a sine regression with my graphic calculator, it returns an error message that says: Singular Matrix

I decided then to do it by hand. Here are three points.

Minimum: (0,554.8), Maximum: (45, 1220.5) and a random point (20, 830.7)

I want something in the format of: A*sin B(x-c) + d

This is what I did, is it correct?

A = (1220.5-554.8)/2
B = (2*pi)/45
D = (1220.5+554.8)/2
C = One unknown, so I used the random point shown to solve:

(Should I have calc in radians or degrees?)

Unless a problem specifically gives a value as the measure of an angle in degrees, you should always use radians. Unfortunately, you don't say how the given information was derived. What are the units for the x variablle? That "45" makes me wonder if it not in degrees. The distance from max to min for a sine function is $\pi$ radians or 180 degrees, NOT $2\pi$ radians or 360 degrees.

YOur formulas for A and D are correct.

30,7

My steps: ( I will use letters for simplicity)

830.7 = A*sinB(x-c)+d
830.7 - D = A*sinB(x-c)
Ans/A = sinB(x-c)
sin^-1(Ans/A) = B(x-c)
Ans/B=x-c
-c=(Ans/B)-x

But I am not getting anything sensible...

Is my calculator right or did I do anything wrong?

Thanks

 

[Peter G.]

So I should do pi over 45 years instead of 2pi over 45?