[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vp / vr / w / wg / wsg / wsr / x / y / ] [Home]
4chanarchives logo

How would you solve this equation system with trigonometric functions? (If it even


Thread replies: 6
Thread images: 1

How would you solve this equation system with trigonometric functions? (If it even have a solution).

$x*(cos(\theta) - 1) + y*(sin(\theta)) = 0 $
$x*(-sin(\theta)) + y*(cos(\theta) - 1) = 0 $

I'm getting the eigenvectors for a rotation matrix. Since I'm such a dumbass with trigonometric functions, it was for me a full challenge to get to the eigenvalues, but I did it with the help of 4chan/sci.

Now I'm stuck again finding the eigenvectors for the corresponding eigenvalues. The equation in the image correspond to an eigenvalue 1 (I get to the equation following some videos in YT on how to find the eigenvectors).

If it's not trouble and someone could at least give me some tip, clue, a trigonometric identity, tell me if I'm missing something obvious or tell me some of that magical things mathematicians do with trigonometric functions.

Thanks in advance.
>>
>>7977245
well, the rotation preserves both x and y
so the angle must be a multiple of 2*pi
>>
I don't know hot to call Tex code here >.<
$x*(cos(\theta) - 1) + y*(sin(\theta)) = 0 $
$x*(-sin(\theta)) + y*(cos(\theta) - 1) = 0 $
>>
>>7977249
let me elaborate. a 2x2 matrix (a linear transformation from R^2 to R^2) which has the form
[ a, b]
[-b, a]
is actually isomorphic to a complex linear transformation from C to C, which is defined by multiplying by (a+bi), or (a-bi) depending on how you want to define i.

so this matrix you're looking at, where T(x, y) = (x, y) is actually the equation

(cost - isent)(x+yi) = x+y
which is exactly
z*e^(it) = z

so e^(it)=1, giving t = k*2pi
>>
>>7977260
equation should be
(cost - isent)(x+yi) = x+yi
>>
>>7977260
nicely done anon.
Thread replies: 6
Thread images: 1
[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vp / vr / w / wg / wsg / wsr / x / y / ] [Home]

All trademarks and copyrights on this page are owned by their respective parties. Images uploaded are the responsibility of the Poster. Comments are owned by the Poster.
If a post contains personal/copyrighted/illegal content you can contact me at [email protected] with that post and thread number and it will be removed as soon as possible.
If a post contains illegal content, please click on its [Report] button and follow the instructions.
This is a 4chan archive - all of the content originated from them. If you need information for a Poster - you need to contact them.
This website shows only archived content and is not affiliated with 4chan in any way.
If you like this website please support us by donating with Bitcoin at 1XVgDnu36zCj97gLdeSwHMdiJaBkqhtMK