I Rotating Coordinates

Nusc

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.

Related Differential Geometry News on Phys.org

FactChecker

Gold Member
2018 Award
Can you please explain your question some more? How could the answer NOT change if you change the equations and the resulting values?

Nusc

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?

Attachments

• 13.7 KB Views: 197

Nusc

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

FactChecker

Gold Member
2018 Award
I still don't understand. In the diagram you posted, where are the points (x,y), (x',y'), and the angle theta?

"Rotating Coordinates"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving