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AQA A Level - Addition Formulae

Trig Addition Formulae & Double Angle Formulae

A2 Revision A2 Revision

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Prove Addition Formulae (A2) Prove Addition Formulae (A2)

Prove addition formulae using geometric construction

sin(2x) (A2) sin(2x) (A2)
cos(2x) (A2) cos(2x) (A2)

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sin(x $\pm$ a) (A2) sin(x $\pm$ a) (A2)

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cos(x $\pm$ a) (A2) cos(x $\pm$ a) (A2)

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a sin x $\pm$ b cos x (A2) a sin x $\pm$ b cos x (A2)

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a cos x $\pm$ b sin x (A2) a cos x $\pm$ b sin x (A2)

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sin(x+a) + sin(x-a) (Ext) sin(x+a) + sin(x-a) (Ext)

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Visualise sin(2x) Double Angle Formulae

The double angle formulae are useful in solving trigonometric formulae. This display allows you to view formulae relating to

\sin (a x)

with

a

an adjustable constant.

Initially,

a

is set to 0 so you can visualise how

\sin (c x) \cos (c x)

arises as the product of

\sin (c x)

and

\cos (c x)

.

Then, by adjusting

a

b

and

c

to make the green and red curves coincide, you can view the double angle formulae, not only for

\sin (2 x)

, but for other values of

a

too.

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Visualise cos(2x) Double Angle Formulae

The double angle formulae are useful in solving trigonometric formulae. This display allows you to view formulae relating to

\cos (a x)

with

a

an adjustable constant.

By adjusting

a

b

c

and

d

to make the green and red curves coincide, you can view the double angle formulae, for

\cos (2 x)

in its different forms.

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Visualise sin(x $\pm$ a) Addition Formulae

This display allows you to visualise the addition formulae:

\sin (x + a) = \sin (x) \cos (a) + \cos (x) \sin (a)

\sin (x - a) = \sin (x) \cos (a) - \cos (x) \sin (a)

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Visualise cos(x $\pm$ a) Addition Formulae

This display allows you to visualise the addition formulae:

\cos (x + a) = \cos (x) \cos (a) - \sin (x) \sin (a)

\cos (x - a) = \cos (x) \cos (a) + \sin (x) \sin (a)

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Visualise a sin x $\pm$ b cos x to sin

This display allows you to visualise the transformations:

a \sin (x) + b \cos (x) = R \sin (x + α)

a \sin (x) - b \cos (x) = R \sin (x - α)

After adjusting

a

and

b

, you can adjust

r

and

α

to their derived values to see the two curves coincide.

For a better view, you should use the navigation buttons in the lower right corner to zoom in and out.

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Visualise a cos x $\pm$ b sin x to cos

This display allows you to visualise the transformations:

a \cos (x) + b \sin (x) = R \cos (x - α)

a \cos (x) - b \sin (x) = R \cos (x + α)

After adjusting

a

and

b

, you can adjust

r

and

α

to their derived values to see the two curves coincide.

For a better view, you should use the navigation buttons in the lower right corner to zoom in and out.

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sin(x + a) + sin(x - a)

The display shows

y = \sin x

in blue and

y = \sin (x + a) + \sin (x - a)

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AQA A Level - Addition Formulae

Trig Addition Formulae & Double Angle Formulae

Prove addition formulae using geometric construction

Visualise sin(2x) Double Angle Formulae

Visualise cos(2x) Double Angle Formulae

Visualise sin(x $\pm$ a) Addition Formulae

Visualise cos(x $\pm$ a) Addition Formulae

Visualise a sin x $\pm$ b cos x to sin

Visualise a cos x $\pm$ b sin x to cos

sin(x + a) + sin(x - a)

A Level Maths Settings

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AQA A Level - Addition Formulae

Trig Addition Formulae & Double Angle Formulae

AQA A2 Syllabus Content - E6

Prove addition formulae using geometric construction

Geogebra Context

Visualise sin(2x) Double Angle Formulae

Notes

Visualise cos(2x) Double Angle Formulae

Notes

Visualise sin(x ± a) Addition Formulae

Notes

Visualise cos(x ± a) Addition Formulae

Notes

Visualise a sin x ± b cos x to sin

Notes

Visualise a cos x ± b sin x to cos

Notes

sin(x + a) + sin(x - a)

Notes

A Level Maths Settings

Current A Level Syllabus

Current Stage

Current Question Difficulty

Current Calculator

Visualise sin(x $\pm$ a) Addition Formulae

Visualise cos(x $\pm$ a) Addition Formulae

Visualise a sin x $\pm$ b cos x to sin

Visualise a cos x $\pm$ b sin x to cos