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Cosine of the Difference of Two Angles

Cosine of the Difference of Two Angles
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2017-07-28 15:58
AngleTrigonometryGeometric Construction
This example illustrates the cosine of the difference of two angles. Key mathematical concepts include the cosine function and angles. Using GeoGebra commands such as Point, Angle, Segment, Rotate, it demonstrates the cosine difference angle formula. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(c) → T
  2. Point(c) → R
  3. Angle((1, 0), (0, 0), T) → α
  4. Angle((1, 0), (0, 0), R) → β
  5. Segment((0, 0), T) → a
  6. Segment((0, 0), R) → b
  7. Segment(R, T) → d
  8. Angle(R, (0, 0), T) → γ
  9. Rotate(T, (-θ)) → S
  10. Rotate(R, (-θ)) → Q
  11. Segment(S, Q) → e
  12. Segment((0, 0), S) → f
  13. Segment((0, 0), Q) → g
  14. Angle(Q, (0, 0), S) → δ

AI Drawing Prompt Reference

Draw a right-angle coordinate system. Mark two points on the x-axis to form angles α and β. Connect the origin to these points to create segments a and b, and connect the points to form segment d. Rotate segments a and b around the origin counterclockwise by -θ to get points S and Q. Connect S and Q to form segment e, and connect the origin to S and Q to form segments f and g. Connect Q and S to form segment δ, illustrating the geometric meaning of the cosine difference angle formula.
The prompt above was compiled from the original drawing commands and is for reference only.