I have the following equation which I believe is approximately valid for my dataset.
$$\frac{L\sin\beta}{s_i} = A\left(\frac{\sin\beta}{RE\cos\beta}\right)^{0.5}$$
where L, $\beta, s_i$, and RE are variables (RE is the Reynolds number); $A$ is a constant.
If I plot the left hand side versus the right hand side without the constant $A$ included on the RHS, I get a reasonably good fit with an $R^2$ valued of $0.939$. However, if I divide both sides by $\sin\beta$, the fit is poor with an R squared value of $0.677$.
$$\frac{L}{s_i} = A\left(\frac{1}{RE\sin\beta \cos\beta}\right)^{0.5}$$
Is this happening because $\sin\beta$ is a variable? The reason I want to divide by $\sin\beta$ is because I think it makes more sense from a physical explanation of the phenomena that has lead to this approximate equation.