\[ \begin{flalign} k=\left[-30...30\right]&& \end{flalign} \] \[ \begin{flalign} \phi=0　　←\ \color{Blue}0\ \le\ \phi\ \le\ 2\pi\ \text{の範囲で振動させる}&& \end{flalign} \] \[ \begin{flalign} x\cos \phi+y\sin \phi=k\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\}&& \end{flalign} \] \[ \begin{flalign} -x\sin \phi+y\cos \phi=k\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\}&& \end{flalign} \] \[ \begin{flalign} x\cos \phi+y\sin \phi=0\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\}&& \end{flalign} \] \[ \begin{flalign} -x\sin \phi+y\cos \phi=0\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\}&& \end{flalign} \]
\( \color{Green}x'= x\ cos\theta-y\ sin\theta　　y'= x\ sin\theta+y\ cos\theta\ 　より、\)
　　　\( \color{Green}x= x'cos\theta+y'sin\theta　　y= -x'sin\theta+y'cos\theta \)
\( \color{Green}これらを　x=0,1,2,・・・　と　y=0,1,2,・・・　に代入して、\)
　　　\( \color{Green}x'cos\theta+y'sin\theta=0,1,2,・・・ 　　-x'sin\theta+y'cos\theta=0,1,2,・・・ \)

コピペ用テキストエリア（ Ctrl＋v で貼り付け ）：

k=\left[-30...30\right] \phi=0 x\cos \phi+y\sin \phi=k\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\} -x\sin \phi+y\cos \phi=k\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\} x\cos \phi+y\sin \phi=0\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\} -x\sin \phi+y\cos \phi=0\ \ \left\{-10\le x\le10\right\}\ \left\{-10\le y\le10\right\}