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Trigonometric Ratios by Jeff Caldwell

Trigonometric Ratios by Jeff Caldwell
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2017-08-18 01:27
AngleTrigonometryGeometric Construction
In collections Unit 9: Right Triangles and Trigonometry
This example demonstrates the basic relationships of trigonometric ratios. It involves core mathematical concepts such as trigonometric functions, angle and side relationships. Using GeoGebra commands like Segment, Rotate, Angle, etc., a triangle is constructed to show the relationship between its sides and angles. Suitable for students at the junior high school level and above to learn the basic properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → AB
  2. Rotate(B, CAB, A) → B'
  3. Angle(B, A, B') → β_2
  4. OrthogonalLine(B, AB) → b
  5. Line(A, B') → c
  6. Intersect(b, c) → C
  7. Segment(A, C) → AC
  8. Segment(B, C) → BC
  9. Angle(C, B, A) → α
  10. Segment(C, B) → f
  11. Segment(A, C) → g
  12. Segment(A, B) → i

AI Drawing Prompt Reference

Draw a right triangle to illustrate the relationships between its angles and side lengths. Start by drawing a straight line, then rotate one end to form a second angle and determine the third vertex. Next, draw a perpendicular line to the straight side and find the intersection with the rotated line to complete the triangle. Finally, connect the midpoint of the hypotenuse to the right angle vertex with a dashed line, and label the lengths of the sides and the measures of the angles to demonstrate the basic trigonometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.