Homepage

Course Index

Build a Quiz

Subscriptions

Courses

NSW Y12 Maths Standard 1 NSW Y12 Maths Standard 2 NSW Y12 Maths Advanced NSW Y12 Maths Extension 1 NSW Y12 Maths Extension 2

Topics

Trig Equations Proof Vectors Calculus Differential Equations Projectile Motion Binomial Distribution Buy Books

NSW Y12 Maths - Extension 1 Trig Functions Auxiliary Angle Method

Resources for Auxiliary Angle Method

  • Questions

    14

    With Worked Solution
    Click Here
  • Video Tutorials

    2


    Click Here
  • HSC Questions

    8

    With Worked Solution
    Click Here

Auxiliary Angle Method Theory

Writing the equation \(a \sin x+b \cos x=c\) in the form \(r \sin (x+\alpha)=c \) or \( r\cos (x-\alpha)=c\) allows you to solve the equation. \\ \textbf{Example}\\ In the domain, \(0 \le \theta \le 2 \pi\), solve \(\sqrt{3} \cos \theta - \sin \theta =1\)\\ \textbf{Solution}\\ $\begin{aligned} \text{Let } \sqrt{3} \cos \theta-\sin \theta & \equiv A \cos (\theta+\alpha)=1 \\ & \equiv A \cos \theta \cos \alpha-A \sin \theta \sin \alpha \end{aligned}$\\ $\begin{aligned} A \cos \alpha &=\sqrt{3} & A \sin \alpha &=1 \\ \cos \alpha &=\frac{\sqrt{3}}{A} & \sin \alpha &=\frac{1}{A} \\ \tan \alpha &=\frac{1}{\sqrt{3}} & \frac{3}{A^2} &+\frac{1}{A^2}=1 \\ \alpha &=\frac{\pi}{6} & A^2 &=4 \\ & &A =2 \end{aligned}$\\ $\begin{aligned} \therefore \quad 2 \cos \left(\theta+\frac{\pi}{6}\right)=1 \\ \quad \cos \left(\theta+\frac{\pi}{6}\right)&=\frac{1}{2} \\ \theta+\frac{\pi}{6}&=\frac{\pi}{3}, \frac{5 \pi}{3} \\ \therefore \theta&=\frac{\pi}{6}, \frac{3 \pi}{2} \end{aligned}$\\

Create account

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Auxiliary Angle Method.

  • Auxiliary Angle Method - Video - The Auxiliary Angle Method 1

  • Auxiliary Angle Method - Video - The Auxiliary Angle Method 2

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

Books / e-books

Course Book

Purchase the course book. This book either comes as a physical book or it can be purchased as an e-book. 

Topic Books

You may choose to purchase the individual topic book from the main coursebook. These only come as e-books. 

 

NSW Year 12 Maths Extension 1 - Trig Equations

Buy

NSW Year 12 Maths Extension 1 - Proof

Buy

NSW Year 12 Maths Extension 1 -Vectors

Buy

 

 

NSW Year 12 Maths Extension 1 - Calculus

Buy

NSW Year 12 Maths Extension 1 -Differential Equations

Buy

NSW Year 12 Maths Extension 1 -Projectile Motion

Buy

 

 

NSW Year 12 Maths Extension 1 -Binomial Distribution

Buy