Course Description

The course covers every dot point from MA-T1 Trigonometry and Measure of Angles and  MA-T2 Trigonometric Functions and Identities. 

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 170 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.

New and existing content is explored in detail, including interesting and more efficient techniques that experienced teachers may not have seen before. Important points to be covered with students are noted, and the limits of the syllabus are discussed. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.

Each lesson includes a section for Extension Students, that covers work that can help them develop skills and techniques that helps prepare them for content they will cover in the Extension 1 or Extension 2 courses.

The course includes:

  • 170 recorded examples
  • 300 page course handout
  • 130 optional practice questions matching the examples from the course
  • 73 mixed questions, all with fully worked solutions.

The remainder of the Year 11 Advanced syllabus will be covered in four other courses:

ADV#1 and  ADV#2 cover MA-F1 Working with Functions

ADV#4 covers MA-C1 Introduction to Differentiation 

ADV#5 covers MA-E1 Logarithms and Exponentials and MA-S1 Probability and Discrete Probability Distributions.

Teaching Standards

2.1.2 Proficient Level - Know the content and how to teach it - Content and teaching strategies of the teaching area:  Apply knowledge of the content and teaching strategies of the teaching area to develop engaging teaching activities.

Do you teach in NSW? If so, this is relevant to you:

Completing Mathematics In Depth - Year 11 Advanced - Trigonometry - ADV#3 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and Assessment of NSW Curriculum/Early Years Learning Framework, addressing Standard Descriptor 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher in NSW.

Course curriculum

  • 1

    Introduction

    • Course Administration

    • Introduction to the Mathematics Advanced Year 11 In Depth Series

    • Introduction to In Depth ADV#3
  • 2

    Trigonometry (Year 11)

    • Introduction to Trigonometry

    • Relevant Parts of the Syllabus
  • 3

    Lesson 1 - Cyclometry

    • Lesson Overview

    • Understanding Trigonometry

    • The Unit Circle and the (very simplified) Origins of Trigonometry

    • Defining Sine

    • Why are Angles Measured Anti-clockwise from the Positive Direction of the 𝑥-axis?

    • Defining Cosine

    • Defining Tangent, Cotangent, Secant and Cosecant

    • Defining Tangent

    • Defining Secant

    • Why can Tangent and Secant Sometimes be Undefined?

    • Defining Cotangent

    • Defining Cosecant

    • Why can Cotangent and Cosecant Sometimes be Undefined?

    • How the Six Intervals Change as the Point Moves

    • Defining Terms - Alternative Diagram

    • Introducing the Angle at the Centre

    • Linking Trigonometric Ratios & Intervals in the Unit Circle

    • Why are Sine, Cosine and Tangent the main three ratios?

    • The Hexagon Mnemonic

    • Examples

    • Extension Students

    • Summary & Practice Exercises

    • ADV#3 Lesson 1 Quiz
  • 4

    Lesson 2 - Right Angled Triangles – Theory

    • Lesson Overview

    • Pythagoras Theorem

    • Calculating Unknown Sides using Pythagoras Theorem

    • Converse of Pythagoras Theorem

    • Naming Sides of a Right Angled Triangle

    • Trigonometric Ratios

    • Degrees, Minutes and Seconds

    • Using the Calculator for Trigonometry

    • Complementary Ratios

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 2 Quiz
  • 5

    Lesson 3 - Right Angled Triangles – Finding Sides and Angles

    • Lesson Overview

    • Finding Unknown Sides or Angles

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 3 Quiz
  • 6

    Lesson 4 - Right Angled Triangles – Exact Ratios

    • Lesson Overview

    • Exact Trigonometric Ratios

    • Finding Unknown Sides or Angles by Scaling the Exact Ratio Triangles

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 4 Quiz
  • 7

    Lesson 5 - Right Angled Triangles – 2D Problem Solving

    • Lesson Overview

    • Applications of Right Angled Trigonometry in 2D

    • Angles of Elevation and Depression

    • Bearings

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 5 Quiz
  • 8

    Lesson 6 - Right Angled Triangles – 3D Problem Solving

    • Lesson Overview

    • Right Angled Trigonometry in 3D

    • Problems Involving 2 right angled triangles

    • Pythagoras Theorem in Three Dimensions

    • Problems Involving 3 right angled triangles

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 6 Quiz
  • 9

    Lesson 7 - Obtuse Angles and The Sine Rule

    • Lesson Overview

    • Non-Right Angled Triangles

    • Trigonometric Ratios for Non-Acute Angles

    • Trigonometric Ratios of Obtuse Angles

    • Method 1: Intervals Around the Unit Circle

    • Method 2: Introducing the Unit Circle

    • Examples

    • Sine Rule

    • Finding Unknown Sides with the Sine Rule

    • Finding Unknown Angles with the Sine Rule

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 7 Quiz
  • 10

    Lesson 8 - The Cosine Rule

    • Lesson Overview

    • Cosine Rule

    • Using the Cosine Rule to find an Unknown Side or Angle

    • Ambiguous Case

    • Other Variations and Applications

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 8 Quiz
  • 11

    Lesson 9 - Area of a Triangle

    • Lesson Overview

    • Area of a Triangle

    • Finding the Area of a Non-right Angled Triangle

    • Using the Area to find a Side

    • Harder Applications

    • Using the Sine or Cosine Rule then the Area Formula

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 9 Quiz
  • 12

    Lesson 10 - Radians

    • Lesson Overview

    • How Should we Measure Angles?

    • Radians

    • Converting Between Degrees and Radians

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 10 Quiz
  • 13

    Lesson 11 - Arc Length & Area of a Sector

    • Lesson Overview

    • Arc Length

    • Area of a Sector

    • Area of a Segment

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 11 Quiz
  • 14

    Lesson 12 - Angles of Any Magnitude

    • Lesson Overview

    • Angles of Any Magnitude

    • Method 1: Intervals Around the Unit Circle - Quick Version

    • Method 1: Intervals Around the Unit Circle - Full Explanation

    • Method 2: The Unit Circle

    • Using Angles of Any Magnitude

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 12 Quiz
  • 15

    Lesson 13 - Trigonometric Graphs

    • Lesson Overview

    • Linking Trigonometric Graphs to the Unit Circle

    • Sketching The Sine Curve

    • Sketching The Cosine Curve

    • Sketching The Tangent Curve

    • Sketching the Curves of the Reciprocal Ratios

    • Examples

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 13 Quiz
  • 16

    Lesson 14 - Simple Trig Equations

    • Lesson Overview

    • Simple Trigonometric Equations

    • Trig Equations Reducible to Quadratic Equations

    • General Solutions

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 14 Quiz
  • 17

    Lesson 15 - Identities, Expressions & Proofs

    • Lesson Overview

    • Trig Identities versus Trig Equations

    • Trigonometric Proofs & Simplifying Expressions

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 15 Quiz
  • 18

    Lesson 16 - Harder Trig Equations

    • Lesson Overview

    • Harder Trig Equations

    • Extension Students

    • Practice Exercises

    • ADV#3 Lesson 16 Quiz
  • 19

    Questions from the HSC

    • Advanced Year 11 Trigonometry in the HSC Exams
  • 20

    Appendix 1: Mixed Revision Exercises

    • Mixed Revision
  • 21

    Appendix 2: Bonus Lesson - A Background to Proof

    • Lesson Overview

    • Proof - The Art of Clear and Logical Argument

    • What is a Proof?

    • Why are Proofs so hard?

    • Rules & Standards

    • Writing a Good Direct Proof

    • Types of Proof

    • Practice Exercises

    • ADV#3 Appendix 2 Quiz
  • 22

    Conclusion

    • Highlights of Trigonometry

    • Conclusion to Year 11 Trigonometry (ADV#3)
  • 23

    Course Feedback

    • Feedback form

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