Relationship between two coordinate systems.

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SUMMARY

The discussion focuses on finding the relationship between two coordinate systems, specifically the u-v coordinate system and its relationship to Cartesian coordinates. The origin of the u-v system is established at (6, 3), and the concept of constraining the v coordinate to zero indicates that the analysis is limited to the u-axis. The use of trigonometric functions, such as sine and cosine, is highlighted to derive the relationships between the coordinates, with sin(35) = (6-x)/u and cos(35) = (y-3)/u being key equations in the solution process.

PREREQUISITES
  • Understanding of coordinate systems, specifically u-v and Cartesian coordinates.
  • Knowledge of basic trigonometry, including sine and cosine functions.
  • Familiarity with right triangle properties and relationships.
  • Ability to interpret geometric representations and diagrams.
NEXT STEPS
  • Study the derivation of relationships in different coordinate systems.
  • Learn about trigonometric identities and their applications in geometry.
  • Explore the concept of vector representation in arbitrary coordinate systems.
  • Investigate the properties of right triangles and their relevance in coordinate transformations.
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Students in mathematics or physics, educators teaching coordinate geometry, and anyone interested in understanding the relationships between different coordinate systems and their applications in solving geometric problems.

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Homework Statement


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The Attempt at a Solution


Could someone please explain what is meant by "if v is constrained to 0"? Also how do you find a relationship between two axis of different coordinate systems? I really have no clue where to start.

Thanks!
 
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Do you know how to find the coordinates of a vector with respect to an arbitrary system?

They're saying to constrain the v coordinate to zero.
 
'v is constrained to 0' means that we are on the u-axis. That's true because they are only asking for the value of u. Note that the origin of the u, v coordinate system is at (x, y)= (6, 3). Dropping a perpendicular from a point on the u axis, that is from (u, 0), to the line x= 6 gives a right triangle with hypotenuse of length u, 'near side' of length y- 3, and 'opposite side' of length 6- x.

The standard trig definitions of sine and cosine give sin(35)= (6-x)/u and cos(35)= (y- 3)/u.
 

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