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# FP3 Trigonometric Series Help watch

1. Sum the following trigonometric series.

(a) sinθ - 1/3 sin2θ + 1/9 sin3θ - 1/27 sin4θ + ...

(b) 1 -
cosθcosθ + cos^2θcos2θ - cos^3θcos3θ +...+ (-1)^n cos^nθcosnθ

I'm pretty much stumped on both and the textbook isn't being particularly helpful
.

The only starting point I can think of for part (a) is that the series is convergent, with a limit 1/(1-(1/3)e^​θi).

Any help would be really appreciated
.
2. (Original post by tbhlouise)
Sum the following trigonometric series.

(a) sinθ - 1/3 sin2θ + 1/9 sin3θ - 1/27 sin4θ + ...

(b) 1 -
cosθcosθ + cos^2θcos2θ - cos^3θcos3θ +...+ (-1)^n cos^nθcosnθ

I'm pretty much stumped on both and the textbook isn't being particularly helpful
.

The only starting point I can think of for part (a) is that the series is convergent, with a limit 1/(1-(1/3)e^​θi).

Any help would be really appreciated
.
sorry to be a pain but
post a picture of the question

what level work is this so I can see what you may use
3. (Original post by TeeEm)
sorry to be a pain but
post a picture of the question

what level work is this so I can see what you may use
Here's the q, it's A Level Further Pure
Attached Images

4. (Original post by tbhlouise)
Here's the q, it's A Level Further Pure
these can be summed by demoivre by turning them into geometric progression of a complex exponential (and occasionally binomials) and then equate real and imaginary parts.

here is 2 examples

pdf.pdf

I hope you work your problems out.

If you have no luck I can run you though one of them tomorrow afternoon after 4 p.m.

.
5. (Original post by TeeEm)
these can be summed by demoivre by turning them into geometric progression of a complex exponential (and occasionally binomials) and then equate real and imaginary parts.

here is 2 examples

pdf.pdf

I hope you work your problems out.

If you have no luck I can run you though one of them tomorrow afternoon after 4 p.m.

.
Thanks . I'll work through them now and hope I get clarity on this topic
6. (Original post by tbhlouise)
Thanks . I'll work through them now and hope I get clarity on this topic
otherwise I will look at one of your questions tomorrow...
way too busy now.
7. (Original post by tbhlouise)
Sum the following trigonometric series.

(a) sinθ - 1/3 sin2θ + 1/9 sin3θ - 1/27 sin4θ + ...

(b) 1 -
cosθcosθ + cos^2θcos2θ - cos^3θcos3θ +...+ (-1)^n cos^nθcosnθ

I'm pretty much stumped on both and the textbook isn't being particularly helpful
.

The only starting point I can think of for part (a) is that the series is convergent, with a limit 1/(1-(1/3)e^​θi).

Any help would be really appreciated
.
You've got the right idea for (a) but you can't have a real series that sums to a complex resuit - you need to multiply your series by i and add to the corresponding series with cosines and then take the imaginary part of the result.

N.B, you might need to multiply the resultant series by to get a more recognizable GP but I haven't worked it through, so that might not be necessary!
8. (Original post by tbhlouise)
Sum the following trigonometric series.

(b) 1 cosθcosθ + cos^2θcos2θ - cos^3θcos3θ +...+ (-1)^n cos^nθcosnθ

I'm pretty much stumped on both and the textbook isn't being particularly helpful
.
1. Handy hint: learn latex.
2. Consider the binomial theorem and "take the real part" trick for b)
9. (Original post by davros)
You've got the right idea for (a) but you can't have a real series that sums to a complex resuit - you need to multiply your series by i and add to the corresponding series with cosines and then take the imaginary part of the result.

N.B, you might need to multiply the resultant series by to get a more recognizable GP but I haven't worked it through, so that might not be necessary!
Thanks, that worked! I got an expression for cosθ+isinθ and multiplied top and bottom by its conjugate and then equated its imaginary part to get the right answer .

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