• Mathematics Extension 1
• Year 12

# Inverse Functions and Inverse Trigonometric Functions

approx. 11 hrs

3 topics

27 concepts

Gain extensive understanding of Inverse Functions and Inverse Trigonometric Functions to approach your HSC examinations with confidence.

Available in
NSW

### Overview

Inverse Functions and Inverse Trigonometric Functions are core concepts in Year 12 Mathematics Extension 1 as defined by the NSW Senior Mathematics syllabus.  We help students find connections between mathematical techniques, results and ideas. We demonstrate how to solve complex problems and communicate ideas and arguments using appropriate notation and graphs.

### Topics & Concepts We Cover

This learning program is made up of the following 3 topics, broken down into 27 concepts.

• #### Inverse Functions 9 concepts

1. Find the domain and range of an inverse function

2. Graph the inverse of a function or relation

3. Finding where a function intersects its own inverse

4. Apply the horizontal line test to check if the inverse of a function is a function

5. Finding the equation of the inverse function

6. Restricting the domain for an inverse function to exist

7. Finding the equation of the inverse function with domain restrictions

8. Proving that an inverse function exists

9. Basic properties of inverse functions

• #### Inverse Trigonometric Functions 4 concepts

1. Domain and range of the sin/cos/tan inverse trigonometric functions

2. Properties of inverse trigonometric functions

3. Deriving the graph of the standard inverse trigonometric functions from the sin/cos/tan functions

4. Proving identities involving the inverse trigonometric functions

• #### Calculus and the Inverse Trigonometric Function 14 concepts

1. Integrating expressions in the standard form for inverse trigonometric functions requiring completing the square

2. Finding the anti-derivative of an inverse trigonometric function by considering a derivative

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

4. Differentiate inverse trigonometric functions involving the product rule

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

6. Sketching curves involving the inverse trigonometric functions

7. Differentiate inverse trigonometric functions with a linear argument

8. Differentiate inverse trigonometric functions involving the chain rule

9. Differentiate inverse trigonometric functions involving the quotient rule

10. Applications of the derivative of inverse trigonometric functions

11. Integrating simple expressions in the standard form for inverse trigonometric functions

12. The relation (dy/dx).(dx/dy) = 1

13. Product rule of differentiation

14. 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 Inverse Functions and Inverse Trigonometric Functions

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

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