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Homework Statement
Well this is technically from a calculus problem but my question focuses only on the trig of the problem so I am posting it here. This is for graphing second degree equations with a nonzero xy
Homework Equations
Given:
[tex] Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0 [/tex]
where [tex] B \neq 0 [/tex]
Use the rotation of axes equations to find an equation where B=0. Equations to do so:
[tex] x = X cos(\alpha) - Y sin(\alpha) [/tex]
and
[tex] y = X sin(\alpha) + Y cos(\alpha) [/tex]
and alpha is given as:
[tex] cot(2\alpha) = \frac{A-C}{B} [/tex]
SO finally my question, how to solve for alpha, I think that I have just forgotten my trig or something here but an attempt I made looks like so:
The Attempt at a Solution
[tex] cot(2\alpha) = \frac {A-C}{B} [/tex]
[tex] 2\alpha = cot^{-1} (\frac {A-C}{B}) [/tex]
[tex] \alpha = \frac {cot^{-1}(\frac{A-C}{B})}{2} [/tex]
and if that is correct that is all good and all but I don't remember how to solve for an inverse cotangent or how to enter it into a graphing calc so if I am right with my equation above then can someone re-enlighten me on this?
Thanks!