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c_hocklandFlag for Greece

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question in polar coordinates

i am going through a solution and there is a part i dont understand

it gives u = x+y
v = x-y

then it converts to polar
x=rcosT
y=rsin¿

so far so good

but then he derives

Vr = ucos¿ +vsinT
V¿ = -usin¿ +vcos¿

how did he get the vr and V¿ ?

any input would be appreciated.
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TommySzalapski
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thank u sir!