• Mathematics Specialist
  • Year 11

Further trigonometry

approx. 14 hrs

8 topics

31 concepts

Gain a detailed understanding of Further Trigonometry to enhance your examination results and develop valuable skills with wide application.

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Further Trigonometry encompasses the foundational components of the study of trigonometry as described in the Mathematics Specialist Syllabus for the Australian curriculum. We work with students to ensure they are able to select and apply rules and processes to answer a variety of questions that include applications of trigonometry in three-dimensions, trigonometric identities, bearings, and non-right-angled trigonometry.

Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 31 concepts.

  • Sums and Differences of Angles 4 concepts

    1. Sums and Differences of angles

    2. Ratios of double angles

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

    4. Auxiliary angle method

  • General Solution of Trigonometric Equations 1 concept

    1. General solution of trigonometric equations

  • 3D Trigonometry 4 concepts

    1. Finding angles between planes inside three-dimensional space

    2. 3D trigonometry where the base triangle is not right-angled

    3. Finding angles and lengths inside various solids

    4. 3D trigonometry where the base triangle is right-angled

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

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

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

  • Trigonometric Ratios, Graphs and the Unit Circle 7 concepts

    1. Exact values of trigonometric ratios including reciprocal functions

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

    3. Reciprocal trigonometric functions

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

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

    6. Use the unit circle and graph trigonometric functions

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

  • 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. Proving a mix of trigonometric identities

    2. The two ratio identities

    3. The three Pythagorean identities

    4. The three identities for complementary angles

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 Further trigonometry


  • 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

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Starting at

$49(inc. GST)

per session

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Access to practice questions

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