(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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:

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fairly simple trig question concerning calculus tools

**Physics Forums | Science Articles, Homework Help, Discussion**