Understanding cot2(theta) = A-C / B

[Terrell]

Homework Statement

How did it go from A'x'^2 + B'x'y' + C'y'^2 + D'x' +E'y' + F = 0 to become B' = 2(C-A)sin(theta)cos(theta) + B(cos^2(theta) - sin^2(theta))?

*this is not an assignment, I am just self studying :P

 

[blue_leaf77]

Expand the top most equation then collect the terms based on the powers of $x'$ and $y'$. To obtain (12), just keep track on the terms in the top most equation which contain $x'y'$.

 

[andrewkirk]

Homework Statement

How did it go from A'x'^2 + Bx'y' + C'y'^2 + D'x' +E'y' + F = 0 to become B' = 2(C-A)sin(theta)cos(theta) + B(cos^2(theta) - sin^2(theta))?

The latter is not a deduction from the former. It is simply a definition, which the author is free to make, as the symbol B' has not been used up to that point.

The deduction is the equation immediately after the 'where...' part.

 

[Terrell]

Expand the top most equation then collect the terms based on the powers of $x'$ and $y'$. To obtain (12), just keep track on the terms in the top most equation which contain $x'y'$.

yes. i got that part, but how do i get from the 2nd equation to the third equation?

 

[Terrell]

The latter is not a deduction from the former. It is simply a definition, which the author is free to make, as the symbol B' has not been used up to that point.

The deduction is the equation immediately after the 'where...' part.

but how do i deduce it? what is step1? i don't know how to start.. from A'x'^2 + B'x'y' + ... + F = 0 to B' = 2(C - A)...

 

[blue_leaf77]

Like andrew has said, $B'$ is just a symbol used to represent the coefficient of $x'y'$. The author could have retained the original form of the coefficient in terms of $A$, $B$, $C$, and $\theta$, but it will require more space. He chose $B'$ as the new coefficient for $x'y'$ because this symbol has not been used in the previous derivation.

 

[Terrell]

i got it! just keep track and combine all the terms with x'y' then equate to zero and simplify. thanks guys!

 

[mkeaudric]

can I get the name of the book?

 

[PeroK]

can I get the name of the book?

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