Question Number 33927 by Tinkutara last updated on 27/Apr/18
Commented by Tinkutara last updated on 27/Apr/18
$${Why}\:{here}\:{x}\:{is}\:{substituted}\:{x}=\frac{{x}+{y}}{\sqrt{\mathrm{2}}}? \\ $$
Commented by Tinkutara last updated on 28/Apr/18
$${But}\:{if}\:{axes}\:{are}\:{rotated}\:{by}\:\theta\:{anticlockwise}, \\ $$$${then}\:\left({x},{y}\right)\:{becomes}\:\left({X}\mathrm{cos}\:\theta−{Y}\mathrm{sin}\:\theta,\right. \\ $$$$\left.{X}\mathrm{sin}\:\theta+{Y}\mathrm{cos}\:\theta\right) \\ $$$${so}\:{we}\:{should}\:{substitute}\:{x}=\frac{{X}−{Y}}{\sqrt{\mathrm{2}}} \\ $$$${Please}\:{correct}\:{me}. \\ $$
Commented by MJS last updated on 27/Apr/18
$$\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{rotation} \\ $$$${x}'={x}\centerdot\mathrm{cos}\:\alpha−{y}\centerdot\mathrm{sin}\:\alpha \\ $$$${y}'={x}\centerdot\mathrm{sin}\:\alpha+{y}\centerdot\mathrm{cos}\:\alpha \\ $$
Commented by MJS last updated on 28/Apr/18
$$\mathrm{axes}\:\mathrm{are}\:\mathrm{rotated}\:\mathrm{clockwise}\:\mathrm{here} \\ $$
Commented by Tinkutara last updated on 28/Apr/18
Why?
Commented by MJS last updated on 28/Apr/18
$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know},\:\mathrm{it}\:\mathrm{says}\:\mathrm{this}:\:``...\mathrm{45}°\:\mathrm{in}\:\mathrm{clockwise} \\ $$$$\mathrm{direction}'' \\ $$