### Course Description

This course covers every dot point from ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities and ME-C1 Rates of Change from the new NSW Year 11 Mathematics Extension 1 syllabus. Please note that only Extension 1 content is covered, not Mathematics Advanced. These topics have Functions and Calculus from Advanced as prerequisites.

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 106 proofs and 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.

The course includes:

• 127 recorded examples

• 139 page course handout

• 127 optional practice questions matching the examples from the course, with fully worked solutions

The remainder of the Mathematics Extension 1 syllabus, is covered in four other courses:

EXT1#1 of the series covers  ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (F1.1: Graphical Relationships)

EXT1#2 of the series covers the remainder of ME-F1 Further Work with Functions plus ME-F2 Polynomials.

Ext1#4 (Year 12) covers ME-P1 Proof by Mathematical Induction and ME-V1 Introduction to Vectors.

Ext1#5 (Year 12) covers ME-T3 Trigonometric Equations, ME-C2 Further Calculus Skills, ME-C3 Applications of Calculus and ME-S1 The Binomial Distribution.

### Audience

Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.

### This Course:

Trigonometry (Year 11) & Rates of Change - EXT1#3

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### Complete Subject:

Extension 1 Mathematics (5 courses)

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

Completing Mathematics Extension 1 Year 11: Trigonometry (Year 11) & Rates Of Change -EXT1#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 descriptors 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

## Course curriculum

• 1

### Introduction

• Introduction to the Mathematics Extension 1 In Depth Year 11 Series

• Introduction to Part III

• 2

### Trigonometry

• Introduction to Trigonometry

• 3

### Trigonometry 1: Cyclometry

• Lesson 1 Overview

• A Deeper Understanding of Trigonometry

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

• The Hexagon Mnemonic

• Examples

• Trigonometric Ratios and Intervals in the Unit Circle

• Example

• Lesson 1 Quiz

• 4

### Trigonometry 2: Inverse Trigonometric Functions - Definitions and Sketching

• Lesson 2 Overview

• Angle Size and Arc Length

• Inverse Sine and Arc Sine

• Inverse Trig Functions

• Inverse Sine Function

• Inverse Cosine Function

• Inverse Tangent Function

• Inverse Trigonometric Ratios for all Intervals

• Examples

• Lesson 2 Quiz

• 5

### Trigonometry 3: Inverse Trigonometric Functions - Further Manipulation

• Lesson 3 Overview

• Function of a Function Background Information

• Trig Function of an Inverse Trig Function

• Examples

• Inverse Trig Function of a Trig Function - Restricted Domain

• Inverse Trig Function of a Trig Function - Full Graphs

• Examples

• Properties of inverse trigonometric functions (with Examples)

• Lesson 3 Quiz

• 6

### Trigonometry 4: Compound Angles

• Lesson 4 Overview

• Compound Angle Results

• Examples

• Alternative Proofs - Sum of Angles

• Lesson 4 Quiz

• 7

### Trigonometry 5: Double Angle Results

• Lesson 5 Overview

• Applications of Compound Angles

• Double Angle Results

• Examples

• Lesson 5 Quiz

• 8

### Trigonometry 6: 𝑡-formulae

• Lesson 6 Overview

• Ratios in terms of the tan of half angles

• Examples

• Lesson 6 Quiz

• 9

### Trigonometry 7: Product to Sum Identities

• Lesson 7 Overview

• Product to Sum Identities

• Examples

• Sum to Product Identities

• Examples

• Lesson 7 Quiz

• 10

### Trigonometry 8 (Optional): Beyond the Syllabus

• Lesson 8 Overview

• Graphing Inverse Trig Function of a Trig Function

• Examples

• Further Trig and Inverse Trig Identities

• Trig Functions in Terms of Each of the Other Ratios (with Example)

• Trig of Inverse Trig Identities (with Example)

• 11

### Rates of Change

• Introduction to Rates of Change

• 12

### Rates of Change 1: Simple Rates of Change

• Lesson 1 Overview

• Rates of Change Background Information

• Graphing a Quantity

• Graphing the Rate of Change

• Examples

• Lesson 1 Quiz

• 13

### Rates of Change 2: Motion along a straight line

• Lesson 2 Overview

• Motion Along a Straight Line

• Motion graphs

• Examples

• Lesson 2 Quiz

• 14

### Rates of Change 3: Simple Exponential Growth and Decay

• Lesson 3 Overview

• Simple Exponential Growth and Decay

• Graphing Simple Exponential Growth and Decay

• Examples

• Lesson 3 Quiz

• 15

### Rates of Change 4: Modified Exponential Growth and Decay

• Lesson 4 Overview

• Modified Exponential Growth Model

• Graphing Modified Exponential Growth and Decay

• Newton’s Law Of Cooling

• Examples

• Lesson 4 Quiz

• 16

### Rates of Change 5: Rates of Change Involving Two or More Variables

• Lesson 5 Overview

• The Chain Rule and Simplifying Related Rates of Change

• Examples

• Lesson 5 Quiz

• 17

### Conclusion

• Highlights of Trigonometry and Rates of Change

• Conclusion to Part III

• 18

### Course Feedback

• Course Feedback

## Presenter Steve Howard

Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.

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