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Defining the Coterminal Angle

Defining the Coterminal Angle
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2016-10-19 04:31
AngleTrigonometryTransformationSlider AnimationGraphing
In collections Trig - Angle Rotation & Unit Circle
① This interactive GeoGebra example visually demonstrates the concept of coterminal angles, including the least positive, greatest negative, and reference angles. ② Core mathematical concepts include standard position of angles, angle periodicity (adding multiples of 360°), and reference angle determination. ③ Construction highlights: uses commands such as Rotate, Angle, CurveCartesian, and Textfield; objects include points O, A, B, M, C, D, E, P, vectors u and v, angles α, β, γ, and numeric values posValue, negValue, and increment; sliders or input boxes allow users to change the number of rotations, dynamically showing positive and negative coterminal angles and the reference angle. ④ Suitable for high school or pre-calculus trigonometry lessons, helping students grasp angle periodicity and standard position, and for self-exploration of coterminal angle patterns.

GeoGebra Commands & Parameters

  1. Rotate(B, a°, O) → A
  2. Vector(C, M) → u
  3. Vector(C', M') → v
  4. Angle(B, O, A) → α
  5. Angle(A, O, B) → β
  6. Vector(O, B) → d
  7. Vector(O, A) → e
  8. CurveCartesian(x(O) + ((size / 100 * cos(i° + shift)) * sqrt(i + shift / °)), y(O) + ((size / 100 * sin(i° + shift)) * sqrt(i + shift / °)), i, 0, a) → b
  9. CurveCartesian(x(O) + ((size / 100 * cos(i° - shift)) * sqrt(abs(i - shift / °))), y(O) + ((size / 100 * sin(i° - shift)) * sqrt(abs(i - shift / °))), i, a, 0) → c
  10. Textfield(increment) → inputBox1
  11. Angle((5, 0), O, A) → γ
  12. Angle((-5, 0), O, A) → γ_1

AI Drawing Prompt Reference

Create an interactive diagram illustrating coterminal angles. Start with a ray from the origin as the initial side, then rotate it to form a terminal side, creating an angle. Use arrow vectors to show both ray directions. Display three angles: the angle from initial to terminal side, its reverse, and the reference angle between the terminal side and the positive or negative x-axis. Include an input box to adjust the number of rotations, dynamically updating the terminal side and showing the least positive, greatest negative, and reference angles. Add two spiral curves extending from the origin, one rotating outward and the other inward, to represent angle periodicity. Label key points and emphasize standard position and periodic angle relationships.
The prompt above was compiled from the original drawing commands and is for reference only.