Double Angle Formulae SL

In this page, we will will learn about the Double Angle Formulae used in Trigonometry. It is actually quite rare that exam questions are solely about these identities, but it is essential that you can use and manipulate them confidently because they are used in so many different parts of the course (so they do come up a lot!). You will learn what they are and how to use them.


Key Concepts

On this page, you should learn about the double angle identities for sine and cosine

\(\large\sin2\theta \equiv 2\sin \theta \cos \theta \)

\(\large{\cos2\theta \equiv \cos^2\theta -\sin^2\theta\\ \cos2\theta \equiv 2\cos^2\theta -1\\ \cos2\theta \equiv 1 -2\sin^2\theta}\)

Summary

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Test Yourself

This quiz is about the Double Angle formulae for sin2x and cos2x
START QUIZ!

Exam-style Questions

Question 1

 

Let f(x) = (cos2x - sin2x)²

a) Show that f(x) can be expressed as 1 - sin4x

b) Let f(x) = 1 - sin4x. Sketch the graph of f for \(0\le x\le \pi \)

Hint

Full Solution

Question 2

 

Solve \(cos2θ=sinθ\) for \(0\le \theta \le 2\pi \)

Hint

Full Solution

Question 3

 

a) Show that \(cos2\theta-3cos\theta+2\equiv 2{ cos }^{ 2 }\theta -3cos\theta +1\)

b) Hence, solve \(cos2\theta-3cos\theta+2=0\) for \(0\le \theta \le 2\pi \)

Hint

Full Solution

 

Question 4

 

Let \(cos\theta=\frac{2}{3}\), where \(0\le \theta \le \frac { \pi }{ 2 } \)

Find the value of

a) \(sin\theta\)

b) \(sin2\theta\)

c) \(sin4\theta\)

Hint

Full Solution

Question 6

MY PROGRESS

How much of Double Angle Formulae SL have you understood?