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Domain & Range of Trigonometric Functions on the Unit Circle

Domain & Range of Trigonometric Functions on the Unit Circle
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2015-02-04 14:24
CircleAngleFunctionTrigonometryGeometric Construction
This example dynamically demonstrates the geometric interpretation of sine and cosine functions on the unit circle by moving point P, clearly showing their domains and ranges. Key concepts include the unit circle, trigonometric functions, angles, domains, and ranges. It uses GeoGebra commands like Point, Intersect, Angle, Segment, and text objects for construction. Suitable for high school mathematics teaching to understand basic properties and geometric background of trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Intersect(c, xAxis, 2) → B
  3. Intersect(xAxis, yAxis) → C
  4. Angle(B, C, A) → θ
  5. Segment(C, A) → r

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. Place a movable point on the circle to represent an angle. From the center, draw a radius segment to this pointhol. Also draw a perpendicular from the point to the x-axis, forming a right triangle. Mark the center, the intersection of the circle with the positive x-axis, and the movable point. Display the angle between the positive x-axis, the radius, and the perpendicular. This construction visually shows the domain and range of sine and cosine functions as the point moves around the circle.
The prompt above was compiled from the original drawing commands and is for reference only.