• Mathematics Advanced
  • Year 12

Trigonometric Functions

approx. 15 hrs

5 topics

32 concepts

Proficiency in Trigonometric Functions is critical to attaining a successful outcome in your HSC examinations.

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The Year 12 Trigonometric Functions for Mathematics Advanced program is aligned with the NSW Mathematics Senior syllabus.   In this program, we explain to students how to use circular measure when applying techniques from the study of trigonometry, geometry and calculus to solve a variety of questions ranging in complexity. 

Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 32 concepts.

  • Degrees and Radians 2 concepts

    1. Converting degrees to radians

    2. Converting radians to degrees

  • Radians and the Circle 6 concepts

    1. Using the area of a segment formula to find unknown quantities

    2. Using the arc length formula to find unknown quantities

    3. Finding the area of a sector using radians

    4. Finding the length of an arc using radians

    5. Finding the area of a segment

    6. Using the area of a sector formula to find unknown quantities

  • Trigonometric Ratios and Radians 4 concepts

    1. Approximations to sin x, cos x, tan x, when x is small

    2. Trigonometric equations for angles of any magnitude in radians

    3. Exact values in radians

    4. Use the result for the function (sin x)/x for the limit as x approaches zero

  • Graphs of Trigonometric Functions 5 concepts

    1. Finding the amplitude of sine or cosine functions

    2. Sketch trigonometric functions with translation

    3. Sketch trigonometric functions with dilation

    4. Finding the period of trigonometric functions

    5. Sketch trigonometric functions with multiple transformations

  • Calculus and the Trigonometric Functions 15 concepts

    1. Differentiate trigonometric functions involving the quotient rule

    2. Finding the volume of solids of revolution using techniques of integration involving the trigonometric functions

    3. Finding the anti-derivative of a trigonometric function by considering a derivative

    4. Integrals involving trigonometric substitution

    5. Integrals of the type f '(x)(f(x))^n dx

    6. Differentiate trigonometric functions involving the chain rule

    7. Integration of (sinx)^2 and (cosx)^2

    8. Differentiate trigonometric functions involving the product rule

    9. Integrating basic trigonometric expressions

    10. Finding the area of regions using techniques of integration involving the trigonometric functions

    11. Application of the derivative of the trigonometric functions

    12. Using the reverse chain rule to integrate trigonometric functions

    13. Differentiate trigonometric functions with linear arguments

    14. Product rule of differentiation

    15. Quotient rule of differentiation

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 Functions


  • 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

Fully flexible

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Access to practice questions

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