This chart gives the step by step construction used above.

No. | Name | Definition |
---|---|---|

1 | Point P_{0} |
Point at (0,2), circle shifted up for clarity |

2 | Circle UnitCircle | Circle with center P_{0} and Radius 1 |

3 | Point P | Draggable Point on UnitCircle |

4 | Text Circle | "Unit Circle Coordinates = (" + (x(P)) + "," + (y(P) - 2) + ")" |

5 | Point P_{1} |
Point at (0,2) + (1,0) |

6 | Angle θ | Angle between P_{1}, P_{0}, P |

7 | Text θ | "θ = " + θ |

- | - | - |

8 | Line L1 | Line through P perpendicular to yAxis |

9 | Point P_{3} |
intersection point of L1, yAxis - P moved to y axis |

10 | Segment sinθ | Segment[P_{3}, P] |

11 | Text sin θ | "sin θ = " + (y(P) - 2) -- Remeber the shift |

12 | Point Sθ | (θ, y(P) - 2) -- Traceable sin point |

- | - | - |

13 | Line L2 | Line through P perpendicular to xAxis |

14 | Line L3 | Line through P_{0}, P_{1} - x axis shifted up through P_{0} |

15 | Point P_{4} |
intersection point of L2, L3 |

16 | Segment cosθ | Segment[P, P_{4}] |

17 | Text cosθ | "cos θ = " + (x(P)) |

18 | Point Cθ | (θ, x(P)) -- Traceable cos point |

- | - | - |

19 | Line L4 | Tangent through P to UnitCircle |

20 | Point P_{5} |
intersection point of L4, L3 -- tangent-secant point |

21 | Segment secθ | Segment[P_{0}, P_{5}] |

22 | Text sec θ | "sec θ = " + (x(P_{5})) |

23 | Segment tanθ | Segment[P, P_{5}] |

24 | Text tan θ | "tan θ = " + ((y(P) - 2) / x(P)) |

- | - | - |

25 | Point P_{6} |
intersection point of L4, yAxis -- cotangent-cosecant point |

26 | Segment cscθ | Segment[P_{6}, P_{0}] |

27 | Text csc θ | "csc θ = " + (y(P_{6}) - 2) |

28 | Segment cotθ | Segment[P, P_{6}] |

29 | Text cot θ | "cot θ = " + (x(P) / (y(P) - 2)) |

Return to the Trig Review Applet.

Return to the Applets for courses below calculus page.

Return to the Calculus Applet page.

Return to the GeoGebra Applet page.Last updated By Mike May, S.J., March 20, 2006.