Dealing with unknown constant within summation.

Question

I want to be able to rearrange the equation so that the constant B is removed form the sine component of the following summation.

 

Example  (i=1 to n) Σ sin(Bx_i)cos(BX_i) = 0?

 

I have all the values of X_i but how can i do the sum without first knowing the constant B?

 

I was hoping to be able to have something like  B*Σsin(X_i)... = 0 etc as this would be easy to summate.

 

Basically i am trying to do a regression with 4 equations and 4 unknown coefficients.

 

I also have cos(BX_i) as well in some of the summations.

Answer 1

Recall that sin(2θ) = 2sinθcosθ 

 

  So,  sin(Bx_i)cos(Bx_i) = ½sin(2Bx_i)

 

Does that help at all?

Answer 2

sin (Bx) ≠ B sin x

On the left B is a phase-shift. on the right B is amplitude.