Solving Trig Transformations: Rotation of a Point

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SUMMARY

The discussion focuses on the mathematical transformation of a point's coordinates during an anticlockwise rotation about the origin in a two-dimensional coordinate system. The new coordinates after rotation by an angle z are defined as x' = xcos(z) - ysin(z) and y' = xsin(z) + ycos(z). Participants emphasize the importance of visualizing the problem through diagrams to better understand the relationships between the original and new coordinates.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine and cosine)
  • Familiarity with coordinate geometry concepts
  • Knowledge of rotation transformations in a Cartesian plane
  • Ability to interpret and create geometric diagrams
NEXT STEPS
  • Study the derivation of rotation matrices in 2D geometry
  • Learn about transformations in linear algebra
  • Explore applications of trigonometric transformations in computer graphics
  • Practice problems involving rotation of points and shapes in coordinate systems
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in understanding coordinate transformations and their applications in various fields such as physics and computer graphics.

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Homework Statement



A point with coordinates x and y is rotated in an anticlockwise direction through an angle z, so that its distance from the origin of the coordinate system remains constant. Show that the new x and y coordinates become

xcosz - ysinz and xcosz + ysinz respectively.

Homework Equations





The Attempt at a Solution



Well I am looking for some advice on how to start this! The wording is confusing to me! To my mind surely if you rotate a point it will be exactly the same? Any help would be supremely appretiated.
 
Physics news on Phys.org
By rotating a point, they mean it is rotated about the origin by a angle z. start by drawing a picture, show the x and y components at each location. Now study the pic until you can identify the relationships.
 

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