The division of two equations.

[Jmancuso]

It says to divide

10.17: Asin pL = V/P*L

by

10.18: Ap cos pL = V/P

but it doesn't explain how that is done or the steps to show that the result of the division is true. Is it possible I could get some additional explanation of how the division takes place.

Thank You!

 

[Dr.Peterson]

They're just dividing each side of [MATH]A\sin(pL) = \frac{V}{P}L[/MATH] by each side of [MATH]Ap\cos(pL) = \frac{V}{P}[/MATH], to get [MATH]\frac{A\sin(pL)}{Ap\cos(pL)} = \frac{\frac{V}{P}L}{\frac{V}{P}}[/MATH].

The LHS becomes [MATH]\frac{A\sin(pL)}{Ap\cos(pL)} = \frac{A}{Ap}\frac{\sin(pL)}{\cos(pL)} = \frac{1}{p}\tan(pL)[/MATH].

The RHS becomes [MATH]\frac{V}{P}L\div\frac{V}{P} = \frac{V}{P}L\cdot\frac{P}{V} = L[/MATH].

So they end up with [MATH]\frac{1}{p}\tan(pL) = L[/MATH], which is equivalent to [MATH]\tan(pL) = pL[/MATH].