• Mathematics Extension 1
  • Year 11

Trigonometric Ratios

approx. 14 hrs

8 topics

30 concepts

Build extensive skills in Trigonometric Ratios to optimise academic outcomes.

Available in


In Trigonometric Ratios students will develop proficiency in selecting and applying rules and processes to answer a range of questions including trigonometric identities, bearings and non-right-angled trigonometry. Students will be also explore 3D problems, sums and differences of angles and more complex solutions to trigonometric equations.

Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 30 concepts.

  • Trigonometric Ratios, Graphs and the Unit Circle 7 concepts

    1. Exact values of trigonometric ratios including reciprocal functions

    2. Reciprocal trigonometric functions

    3. Find the exact value of a trigonometric ratio given another trigonometric ratio

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

    5. Use the unit circle and graph trigonometric functions

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

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

  • Solving Trigonometric Equations 2 concepts

    1. Trigonometric equations with compound angles

    2. Solve trigonometric equations with one trigonometric function across a specified domain using the related angle

  • Trigonometric Identities 4 concepts

    1. The two ratio identities

    2. The three identities for complementary angles

    3. Proving a mix of trigonometric identities

    4. The three Pythagorean identities

  • Bearings 3 concepts

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

    2. Solve worded problems involving bearings using SOH CAH TOA

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

  • Non-Right-Angled Triangles 6 concepts

    1. Solve complex bearings problem involving non-right-angled triangles

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

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

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

    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

  • 3D Trigonometry 3 concepts

    1. 3D trigonometry where the base triangle is not right-angled

    2. Finding angles and lengths inside various solids

    3. 3D trigonometry where the base triangle is right-angled

  • Sums and Differences of Angles 4 concepts

    1. Sums and Differences of angles

    2. Application of the t (or half-angle) formula to solve complex trigonometric equations

    3. Auxiliary angle method

    4. Ratios of double angles

  • General Solution of Trigonometric Equations 1 concept

    1. General solution of trigonometric equations

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 Trigonometric Ratios


  • 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

Add your payment details securely online

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

Access to practice questions

Not sure if this program is right for you?

Ask us, we'll help you find the right program.

Enquire now