Homepage

Course Index

Build a Quiz

Subscriptions

Courses

NSW Y11 Maths Standard NSW Y11 Maths Advanced NSW Y11 Maths Extension 1

Topics

Functions Polynomials Inverse Trig Functions and Identities Rates of Change Permutations and Combinations

NSW Y11 Maths - Extension 1 Inverse Trig Functions and Identities Inverse Trig Functions

Resources for Inverse Trig Functions

  • Questions

    45

    With Worked Solution
    Click Here
  • Video Tutorials

    1


    Click Here
  • HSC Questions

    9

    With Worked Solution
    Click Here

Inverse Trig Functions Theory

NSW Syllabus Reference

NSW Syllabus Reference: ME-T1 Inverse Trigonometric Functions. This will require student to 

  • define and use the inverse trigonometric functions (ACMSM119)
  • sketch graphs of the inverse trigonometric functions
  • use the relationships \(\sin(\sin ^{-1}x)=x\) and \(\sin^{-1}(\sin x) =x\), \(\cos(\cos ^{-1}x)=x\) and \(\cos^{-1}(\cos x) =x\), \(\tan(\tan ^{-1}x)=x\) and \(\tan^{-1}(\tan x) =x\) where appropriate, and state the values of \(x\) for which these relationships are valid
  • prove and use the properties: \(\sin^{-1}(-x)=-\sin^{-1}x,\, \cos^{-1}(-x)=\pi -\cos^{-1}x,\, \tan^{-1}(-x)=- \tan ^{-1}x\) and \(\cos^{-1}x+ \sin^{-1}x=\dfrac{\pi}{2}\)
  • solve problems involving inverse trigonometric functions in a variety of abstract and practical situations

Ref: https://educationstandards.nsw.edu.au/

Create account

Access content straight away with a two week free trial

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Inverse Trig Functions.

  • Inverse Trig Functions - Video - Inverse Trig Functions With Double Angle Formulas and Half Angle Identities

    You must be logged in to access this resource

Plans & Pricing

With all subscriptions, you will receive the below benefits and unlock all answers and fully worked solutions.

  • Teachers Tutors
    Features
    Free
    Pro
    All Content
    All courses, all topics
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Quizbuilder
     
    Class Results
     
    Student Results
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions
  • Awesome Students
    Features
    Free
    Pro
    Content
    Any course, any topic
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Basic Results
     
    Analytics
     
    Study Recommendations
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions

Theory

Corresponding to each of the six trigonometric functions \(y = \sin x\), \(y = \cos x\), \(y = \tan x\), \(y = cosec x\), \(y = \sec x\) and \(y = \cot x\) there are six associated inverse trigonometric functions.

In general, if \(y = f(x)\) is a function, then for each \(x\) in the domain, there is one and only one value of \(y\). The relation obtained by interchanging \(x\) and \(y\) is \(x = f(y)\). If for each \(x\) in the domain, \(y\) is uniquely determined, then this represents a new function, called the inverse function to \(y = f(x)\) and is denoted by \(y = {f^{ - 1}}(x)\).

To obtain the inverse function \(y = {f^{ - 1}}(x)\) from \(y = f(x)\), \(x\) and \(y\) are interchanged and consequently, so are the domains and ranges.

The domain of \(y = {f^{ - 1}}(x)\) is the range of \(y = f(x)\) and the range of \(y = {f^{ - 1}}(x)\) is the domain of \(y = f(x)\).

The notation used for the inverse trigonometric functions are

  • If \(y = \sin x\) then the inverse function is \(y = {\sin ^{ - 1}}x\)

  • If \(y = \cos x\) then the inverse function is \(y = {\cos ^{ - 1}}x\)

  • If \(y = \tan x\) then the inverse function is \(y = {\tan^{ - 1}}x\)

  • If \(y = cosec x\) then the inverse function is \(y = {cosec ^{ - 1}}x\)

  • If \(y = \sec x\) then the inverse function is \(y = {\sec ^{ - 1}}x\)

  • If \(y = \cot x\) then the inverse function is \(y = {\cot ^{ - 1}}x\)