# Year 11 – 14: Periodic Phenomena Mathematics – Northern Territory (NT)

### NT Year 11 – 14: Periodic Phenomena Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Year 11 – 14: Periodic Phenomena | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Trig complementary angles | Complementary angle results. | |

Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||

3 | Trig identities | Trigonometric identities | |

Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities. | |||

4 | Trig larger angles | Angles of any magnitude | |

Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle. | |||

5 | Trig larger angles | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees. | |||

6 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |

Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||

7 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||

8 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||

9 | Trig larger angles | Using one ratio to find another. | |

Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude. | |||

10 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

11 | Trig equations | Solving trigonometric equations – Type II. | |

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||

12 | Trig equations | Solving trigonometric equations – Type III. | |

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||

13 | Trigonometry | Sin(A+B) etc sum and difference identities (Stage 2) | |

Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios. | |||

14 | Trigonometry | Double angle formulas (Stage 2) | |

Objective: On completion of the lesson the student will derive and use the double angle trig identities. | |||

15 | Trigonometry | Half angle identities (Stage 2) | |

Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities. | |||

16 | Trigonometry | t Formulas (Stage 2) | |

Objective: On completion of the lesson the student will solve trig equations using the t substitution. | |||

17 | Polar coordinates | Plotting polar coordinates and converting polar to rectangular | |

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system. | |||

18 | Polar coordinates | Converting rectangular coordinates to polar form | |

Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates. | |||

19 | Exam | Exam – Year 11 – 14: Periodic Phenomena | |

Objective: Exam |