Maths and Computing:Trigonometric Series

Trigonometric Series Compound Angle

Expression for cos(mx) in terms of powers of cos(x)

Workings use de Moivre's Theorem

Expression for sin(mx) in terms of powers of cos(x)and powers of sin(x)

Workings use de Moivre's Theorem

Expression for cosⁿ(x) in terms of the sum of compound angles of cos(x)/h3>

Workings use de Moivre's Theorem

Expression for sinⁿ(x) in terms of the sum of compound angles of cos(x) and sin(x)/h3>

Workings use de Moivre's Theorem

Expression for

n	C(n,r)cos(rx)
Σ
r = 0

Expression for

n	C(n,r)sin(rx)
Σ
r = 0

Expression for

∞	a^rcos(rx)
Σ
r = 0

Expression for

∞	a^rsin(rx)
Σ
r = 0

Trigonometric Series

Maths and Computing:

Trigonometric Series Compound Angle

Expression for cos(mx) in terms of powers of cos(x)

Workings use de Moivre's Theorem

Select a value for m

m:

Expression for sin(mx) in terms of powers of cos(x)and powers of sin(x)

Workings use de Moivre's Theorem

Select a value for m

m:

Expression for cosn(x) in terms of the sum of compound angles of cos(x)/h3>

Workings use de Moivre's Theorem

Select a value for n

n:

Expression for sinn(x) in terms of the sum of compound angles of cos(x) and sin(x)/h3>

Workings use de Moivre's Theorem

Select a value for n

n:

Expression for

n

C(n,r)cos(rx)

Σ

r = 0

Select a value for n

n:

Expression for

n

C(n,r)sin(rx)

Σ

r = 0

Select a value for m

m:

Expression for

∞

arcos(rx)

Σ

r = 0

Select values for the nominator and denominator for a. -1 < a < 1

a:

/

Expression for

∞

arsin(rx)

Σ

r = 0

Select a value for a

a:

/

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Expression for cosⁿ(x) in terms of the sum of compound angles of cos(x)/h3>

Expression for sinⁿ(x) in terms of the sum of compound angles of cos(x) and sin(x)/h3>

a^rcos(rx)

a^rsin(rx)