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Question Number 33927 by Tinkutara last updated on 27/Apr/18

Commented by Tinkutara last updated on 27/Apr/18

$$Whyherexissubstitutedx=\frac{x+y}{\sqrt{2}}?$$

Commented by Tinkutara last updated on 28/Apr/18

$$Butifaxesarerotatedby\theta anticlockwise,$$$$then(x,y)becomes(X\cos \theta -Y\sin \theta ,$$$$X\sin \theta +Y\cos \theta )$$$$soweshouldsubstitutex=\frac{X-Y}{\sqrt{2}}$$$$Pleasecorrectme.$$

Commented by MJS last updated on 27/Apr/18

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{rotation}$$$$x^{\prime }=x\cdot \cos \alpha -y\cdot \sin \alpha$$$$y^{\prime }=x\cdot \sin \alpha +y\cdot \cos \alpha$$

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

$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know},\mathrm{it}\mathrm{says}\mathrm{this}:‘‘...45°\mathrm{in}\mathrm{clockwise}$$$${\mathrm{direction}}^{″}$$

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