Understanding cot2(theta) = A-C / B

  • Thread starter Terrell
  • Start date
  • #1
317
26

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, im just self studying :P
 

Attachments

  • cot2theta2.png
    cot2theta2.png
    167.6 KB · Views: 814
Last edited:

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
2,637
785
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'##.
 
  • #3
andrewkirk
Science Advisor
Homework Helper
Insights Author
Gold Member
3,908
1,468

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.
 
  • #4
317
26
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?
 
  • #5
317
26
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)...
 
  • #6
blue_leaf77
Science Advisor
Homework Helper
2,637
785
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.
 
  • #7
317
26
i got it! just keep track and combine all the terms with x'y' then equate to zero and simplify. thanks guys!
 

Related Threads on Understanding cot2(theta) = A-C / B

  • Last Post
Replies
2
Views
28K
Replies
2
Views
171
  • Last Post
Replies
3
Views
1K
Replies
3
Views
627
Replies
9
Views
413
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
7
Views
456
  • Last Post
Replies
1
Views
868
  • Last Post
Replies
3
Views
2K
Top