Talk:Rotation of axes in two dimensions

Mistake in formula

you have a mistake in your rotation formula:

x = x'cos(theta) - y'sin(theta) is right, but

y = x'cos(theta) + y'cos(theta) is wrong, coeff. for x' should be sin(theta)

< this is obvious, how can you have 3 cos(theta) in the equations, symmetry is destroyed!> — Preceding unsigned comment added by 63.166.226.88 (talk) 16:42, 19 October 2006 (UTC)

C and D terms

When you are doing the derivation for the rotation formula and then you expand it in the second step, where do all your C - terms go? Where is the Cx'sin@^2 + Cy'cos@^2 + 2Cx'y'sin@cos@ ?? It is missing! Jkeesh 22:50, 6 March 2007 (UTC) JKEESH

And the expansion of the terms in the derivation is missing the D term or parentheses and the expansion is just basically wrong. Jkeesh 22:58, 6 March 2007 (UTC) JKEESH

Is there a quicker way to calculate the rotated equation instead of having to use all those annoying substitutions? —Preceding unsigned comment added by 70.250.214.9 (talk) 12:25, 22 April 2008 (UTC)

Multiple issues

• In the lead, "counterclockwise" should be removed, for generality.
• The sections Rotation of loci, Elimination of the xy term by the rotation formula and Derivation of the rotation formula should probably be removed altogether, as an article about rotation of axes should not need lengthy derivations.
• Probably most important is that the article specifically addresses the rotation of conic sections but says nothing about a general rotation of coordinates, or linear maps, or matrices, or spaces of more than two dimensions. — Anita5192 (talk) 06:29, 19 July 2015 (UTC)

 Done The article has now been cleaned up. Hopefully this describes the actual subject well but still preserves the treatment that was in the original article without the text being entirely about conic sections. The diagram is not perfect but is the best that I could find. An ideal diagram should also depict the x, y, x' and y' coordinates of the point, label the point P, and label the angle between x and r as $\alpha$. I left the word "counterclockwise" in the lead, since it is common in textbooks to refer to a counterclockwise rotation as standard. — Anita5192 (talk) 20:35, 24 July 2015 (UTC)

Trig formulae

A learner reading this may be baffled by equations (3) and (4). They make use of the standard formulae for addition and subtraction of sines and cosines, but there is no reference to this, and they are not everyday knowledge to the man on the street. Presumably they are explained somewhere else on Wiki, so a cross-reference would be useful.109.150.6.231 (talk) 14:02, 12 February 2020 (UTC)

 Fixed Thank you for pointing this out! —Anita5192 (talk) 16:06, 12 February 2020 (UTC)

Why the page move?

This article was originally called Rotation of axes and discussed the rotation of any number of axes. The article still discusses the rotation of any number of axes. So why change the name?—Anita5192 (talk) 04:46, 17 May 2023 (UTC)

Counterclockwise only?

The first paragraph says counterclockwise rotation. However, the rotation can be clockwise as well, in which case the value of $\theta$ is negative. --Roland (talk) 02:07, 7 September 2024 (UTC)

 Fixed I edited the lead. Hopefully this will make things more clear. — Anita5192 (talk) 02:52, 7 September 2024 (UTC)