• Year 10

# Trigonometry

approx. 16 hrs

9 topics

33 concepts

Develop mastery in Trigonometry to enhance your exam results.

Available in
NSW

### Overview

Year 10 Trigonometry covers the fundamental principles of measurement with triangles and aligns with the Measurement and Geometry Strand in the NSW Mathematics syllabus. In Year 10 Advanced Trigonometry, we help you to become proficient in selecting and applying rules and processes to find unknown angles and side lengths. These skills need to be applied to solve problems involving bearings and angles of elevation and depression. In addition, we help develop an understanding of the trigonometric ratios in terms of the unit circle and its application to solving angles of any magnitude.

### Topics & Concepts We Cover

This learning program is made up of the following 9 topics, broken down into 33 concepts.

• #### Defining Trigonometric Ratios 2 concepts

1. Define the sine, cosine and tangent ratios for angles in right-angled triangles

2. Identify the hypotenuse, adjacent sides and opposite sides on a right angles triangle

• #### Finding Unknown Sides and Angles 6 concepts

1. Rounding angles to the nearest degree, minute or second

2. Find the size in degrees of unknown angles using SOH CAH TOA in right-angled triangles

3. Find the lengths of unknown sides in right-angled triangles using SOH CAH TOA where the given angle is measured in degrees

4. Use the calculator to find unknown angles using sine, cosine and tangent functions

5. Find the lengths of unknown sides in right-angled triangles using SOH CAH TOA where the given angle is measured in degrees and minutes

6. Find the size in degrees and minutes of unknown angles using SOH CAH TOA in right-angled triangles

• #### Angles of Elevation and Depression 1 concept

1. Solve a variety of practical problems involving angles of elevation and depression of right-angled triangles

• #### Introduction to Bearings 4 concepts

1. Construct a bearing diagram from a worded problem

2. Calculate a bearing from a given diagram

3. Interpret three-figure (or true) bearings and compass bearings

4. Solve worded problems involving bearings using SOH CAH TOA

• #### Trigonometry in 3D 1 concept

1. Apply trigonometry in three-dimensions

• #### Unit Circle and Trigonometric Ratios 8 concepts

1. The four quadrants

2. Prove the relationships between the sine and cosine ratios of complementary angles in right-angled triangles

3. Determine the angle of inclination of a line on the Cartesian plane

4. Prove and apply the tangent ratio identity

5. Trigonometric ratios of obtuse angles

6. Determine the possible acute and/or obtuse angle(s), given a trigonometric ratio

7. Use the unit circle to redefine the sine, cosine and tangent ratios

8. Using a reference (or related) angle to find angles of any magnitude

• #### Simple Trigonometric Equations 2 concepts

1. Solve simple trigonometric equations involving only sin/cos/tan

2. Exact values of trigonometric ratios

• #### Graph Trigonometric Functions using the Unit Circle 3 concepts

1. Investigate graphs of the sine, cosine and tangent functions for angles of any magnitude

2. Use the unit circle and graph trigonometric functions

3. Compare the features of trigonometric curves, including periodicity and symmetry

• #### Trigonometry of Non-Right-Angled Triangles 6 concepts

1. Find a side length given the area of a non-right-angled triangle

2. Use the sine area formula to find the area of a non-right-angled triangle

3. Use the cosine rule to find unknown sides and angles of a non-right-angled triangle

4. Solve worded problems involving bearings and angles of elevation and depression of non-right-angled triangles

5. Apply the appropriate rule to find unknowns in non-right-angled triangles

6. Use the sine rule to find unknown sides and angles of a non-right-angled triangle including the ambiguous case

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Trigonometry

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime