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

Sequences and Series Graphs and Equations Differential Calculus Integration Exponential and Log Function Trig Functions Motion and Rates Series and Finance Descriptive Statistics Bivariant Data Analysis Random Variables

NSW Y12 Maths - Advanced Trig Functions Applications of Differentiation of Trig Functions

Resources for Applications of Differentiation of Trig Functions

  • Questions

    14

    With Worked Solution
    Click Here
  • Video Tutorials

    1


    Click Here
  • HSC Questions

    4

    With Worked Solution
    Click Here

Applications of Differentiation of Trig Functions Theory

Applications of the differentiation of trigonometric functions involves determining equations of tangents and normals and stationary points on these functions.\\ \begin{multicols}{2} \textbf{Example 1}\\%31067 Consider the function \(y = \sin x + \cos 2x\). Find the equation of the tangent to the graph of the function at \(x = \dfrac{\pi}{6}\).\\ \textbf{Example 1 solution}\\ $\begin{aligned} y &= \sin x + \cos 2x\\\frac{dy}{dx} &= \cos x -2\sin 2x\\\text{at } x = \frac{\pi}{6} \qquad \frac{dy}{dx} &= \cos\frac{\pi}{6} - 2\sin\frac{\pi}{3}\\&= \frac{\sqrt{3}}{2} - 2\times\frac{\sqrt{3}}{2}\\&= -\frac{\sqrt{3}}{2}\\\text{and } y &= \sin \frac{\pi}{6} +\cos\frac{\pi}{3}\\&= \frac{1}{2} + \frac{1}{2}\\&= 1 \end{aligned}$\\ $\begin{aligned}\therefore \text{ the equation} &\text{ of the tangent is }:\\ y - 1 &= -\frac{\sqrt{3}}{2}\left(x - \frac{\pi}{6}\right)\\y -1 &= -\frac{\sqrt{3}}{2}x + \frac{\sqrt{3}\pi}{12}\\y &= -\frac{\sqrt{3}}{2}x + \frac{\sqrt{3}}{12}\pi + 1\end{aligned}$\\ \columnbreak \textbf{Example 2}\\%24815 Find the equation of the normal to the curve \(y = 2\sin 2x\) at \(x = \dfrac{\pi }{2}\)\\ \textbf{Example 2 solution}\\ $\begin{aligned} y &=2 \sin 2 x \\ y^{\prime} &=2 \cos 2 x \times 2 \\ &=4 \cos 2 x \\ \text{At}\ x &=\pi / 2, y=2 \sin \pi=0 \\ y^{\prime} &=4 \cos \pi=-4 \\ y-0 &=\frac{1}{4}\left(x-\frac{\pi}{2}\right) \\ 4 y &=x-\frac{\pi}{2} \\ x &-4 y-\frac{\pi}{2}=0 \end{aligned}$\\ \end{multicols}

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 Applications of Differentiation of Trig Functions.

  • Applications of Differentiation of Trig Functions - Video - Derivative Rules with TRIG functions

    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