1. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Double Angle Formulae
Objectives:
To recognise and learn the double angle formulae for Sin 2A, Cos 2A and Tan 2A.
To apply the double angle formulae to solving trig equations and proving trig identities.

2. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
SUMMARY
The double angle formulae are:

3. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Activity:
Trig double angle
Card match

4. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
N.B. The formulae link any angle with double the angle.
For example, they can be used for
and
and
and
and
We use them
to solve equations
to prove other identities
to integrate some functions

5. Using double angle formulae to solve equations
4/28/2017
Using double angle formulae to solve equations
We can use the double angle formulae to solve equations involving multiple angles. For example: 5

6. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Solution: or
ANS:

7. Using double angle formulae to prove identities
4/28/2017
Using double angle formulae to prove identities
We can use the double angle formulae to prove other identities involving multiple angles. For example: 7

8. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Exercise
Prove the following identities: 1. 2.

9. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Solutions:
1. Prove
Proof:
l.h.s.
(double angle formulae)
= r.h.s.

10. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Solutions:
2. Prove
l.h.s.
Proof:
(double angle formulae)
= r.h.s.

11. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Activity:
True or false
worksheet

16. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
SUMMARY
The double angle formulae are:

17. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
N.B. The formula link any angle with double the angle.
For example, they can by used for
and
We use them
to solve equations
to prove other identities
to integrate some functions

18. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
Proof:
l.h.s. =
= r.h.s.
e.g. Prove that
(addition formula)
(double angle formulae)

19. Bilborough College Maths - core 4 double angle formulae (Adrian)
28/04/2017
SUMMARY
The rearrangements of the double angle formulae for are
They are important in integration so you should either memorise them or be able to obtain them very quickly.