This document provides rules and formulae for double angles in trigonometry. It contains: 1) Formulae for sin(A+B), cos(A+B), sin2A, and cos2A in terms of sinA, cosA, sinB, and cosB. 2) Examples of using the double angle formulae to find sin2A and cos2A when given sinA and cosA. 3) Alternative versions of the cos2A formula as cos2A = 1 - 2sin2A or cos2A = 2cos2A - 1, which are useful for trigonometric equations.

1. Block 2
Double Compound Angle
Formulae

2. What is to be learned?
• Rules for double angles!!!!!

3. Sin(A + B) =
Sin(A + A) =
sin2A =
SinA CosBSinA CosB + CosA SinB+ CosA SinB
SinA CosASinA CosA + CosA SinA+ CosA SinA
2SinA CosA2SinA CosA

4. Cos(A + B) =
Cos(A + A) =
Cos2A =
CosA CosBCosA CosB –– SinA SinBSinA SinB
CosA CosACosA CosA –– SinA SinASinA SinA
CosACosA –– SinASinA( )2 ( )22 2

5. Double Angle Formulae
If we have two equal angles
sin2A =
Cos2A =
2SinA CosA2SinA CosA
CosACosA( )2
( )2
- SinA- SinA
Cos ACos A –– Sin ASin A2 2
written as
on formula sheet

6. cos A = 2
/√13
Find sin 2A and Cos 2A
Sin2A = 2sinAcosA
= 2 X
Cos2A = Cos2
A – Sin2
A
=
=
=
A2
√133
sinA = 3
/√13
3
/√13 X 2
/√13
= 12
/13
(2
/√13)2
– (3
/√13)2
4
/13
– 9
/13
-5
/13

7. 1 – Sin2
A
1 – Sin2
A – Sin2
A
CosCos22
AA –– SinSin22
AACos2A =
CosCos22
A =A =
Cos2A =
= 1 – 2Sin2
A
1 – Cos2
ASinSin22
A =A =
Cos2A = CosCos22
AA –– (1 – Cos2
A)
= 2Cos= 2Cos22
A – 1A – 1

8. Cos2A = 1 – 2Sin2
A
= 2Cos= 2Cos22
A – 1A – 1
Cos 2A Other versions
and Cos2A
handy for trig equations
also on formula sheet