Rotation of Axis to Eliminate Cross-Product Term

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SUMMARY

The discussion focuses on the mathematical technique of rotating axes to eliminate the cross-product term in a given equation. The user seeks clarification on determining the angles 2θ = π/3 and θ = π/6, as well as the origins of the values √3/2 and 1/2. The solution involves understanding the properties of a 30-60-90 triangle, which provides the necessary trigonometric ratios for these angles. The user is encouraged to visualize the problem using the provided diagrams for better comprehension.

PREREQUISITES
  • Understanding of trigonometric functions and their values for common angles
  • Familiarity with the concept of rotating axes in coordinate geometry
  • Knowledge of 30-60-90 triangles and their properties
  • Basic algebraic manipulation skills for expanding equations
NEXT STEPS
  • Study the properties of 30-60-90 triangles and their trigonometric ratios
  • Learn about coordinate transformations and their applications in eliminating cross-product terms
  • Explore the derivation of trigonometric identities relevant to angle rotation
  • Practice problems involving axis rotation in various mathematical contexts
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in mastering techniques for simplifying equations through axis rotation.

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Homework Statement



The question si the make a rotation of axis to elmininate the cross-product term in the work i provided in this pic: http://img295.imageshack.us/img295/9579/untitledtu4.png

Homework Equations





The Attempt at a Solution



I've drawn of the example in the pic I've given a link.

my questions:

how do i know that 2 theta = pi/3 and theta is pi/6

where does the sqrt(3)/2 and 1/2 come from?

i know there is some kind of 30/60/90 triangle going on here i think.
can someone please help me understand where the numbers are coming from.

if you expand the pic its MUCH easier to view.

thankyou.
 
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a response in your method =p

http://img96.imageshack.us/img96/1745/sresponsewm5.jpg
 
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