Partially rotated coordinate systems

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SUMMARY

The discussion centers on the mathematical derivation of partially rotated coordinate systems, specifically the transformation equations x' = x cos(θ) + y sin(θ) and y' = y cos(θ) - x sin(θ). These equations are crucial for understanding the rotation of axes in the context of special relativity. The user seeks clarity on these transformations to aid in deriving relevant formulas. A reference to a proof is provided from a calculus resource for further study.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Familiarity with coordinate systems and transformations
  • Basic knowledge of special relativity concepts
  • Ability to interpret mathematical proofs
NEXT STEPS
  • Study the derivation of rotation matrices in linear algebra
  • Explore the implications of coordinate transformations in special relativity
  • Learn about the geometric interpretation of trigonometric identities
  • Review the application of rotation of axes in physics problems
USEFUL FOR

Students of physics and mathematics, particularly those focusing on special relativity and coordinate transformations, will benefit from this discussion.

Bassalisk
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Hello,

I am trying to understand this partially rotated coordinate systems.

I do not understand how does x'=xcos(theta)+ysin(theta) and y'=ycos(theta)-xsin(theta)

I am probably stuck at silly answer but i need this to understand deriving of formulas for special relativity.

Thanks
 

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