# Rotating Coordinates

• I
If one rotates a tangent plane on a curved surface, this point can be expressed as follows:

x' = x cos(theta) - y sin(theta)
y' = x sin(theta) + y cos(theta)

One solves for x and y and computes based on the deviation of the deviation.

My question is: would the answer differ if you choose a different point say:

x' = x cos(theta) + y sin(theta)
y' = - x sin(theta) + y cos(theta)

note the negative sign.

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Can you please explain your question some more? How could the answer NOT change if you change the equations and the resulting values?

Can you please explain your question some more? How could the answer NOT change if you change the equations and the resulting values?
In the attached drawing, I can could approach this new point as

x' = x cos(theta) - y sin(theta)
y' = x sin(theta) + y cos(theta)

or

x' = x cos(theta) + y sin(theta)
y' = - x sin(theta) + y cos(theta)

From what you see in the diagram, how would you justify which coordinates?

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If you cannot, then what should the second pair of coordinates look like visually?

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