# De Moivres Theorem Q

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Hi

Could anyone help me get started with this question please?

I understand how to do it for example with cos^5x or sin^3x but I'm not sure what to when they're multiplied together as in question 6 below...

Thanks in advance!

Could anyone help me get started with this question please?

I understand how to do it for example with cos^5x or sin^3x but I'm not sure what to when they're multiplied together as in question 6 below...

Thanks in advance!

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#2

(Original post by

Hi

Could anyone help me get started with this question please?

I understand how to do it for example with cos^5x or sin^3x but I'm not sure what to when they're multiplied together as in question 6 below...

Thanks in advance!

**jamiet0185**)Hi

Could anyone help me get started with this question please?

I understand how to do it for example with cos^5x or sin^3x but I'm not sure what to when they're multiplied together as in question 6 below...

Thanks in advance!

http://www.cosmicriver.net/uploads/5.../algebra8b.pdf

If so, just multiply the cos^4 and sin^3 expressions together.

Last edited by mqb2766; 4 weeks ago

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#3

**jamiet0185**)

Hi

Could anyone help me get started with this question please?

I understand how to do it for example with cos^5x or sin^3x but I'm not sure what to when they're multiplied together as in question 6 below...

Thanks in advance!

Maybe manipulation using this may help you express the integrand in terms of powers of sines and then you may be able to integrate term by term

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(Original post by

Not sure what you've covered? Does (z+/-1/z) mean anything?. If so, just multiply the cos^4 and sin^3 expressions together.

**mqb2766**)Not sure what you've covered? Does (z+/-1/z) mean anything?. If so, just multiply the cos^4 and sin^3 expressions together.

Yeah, it does mean something to me.

I thought about multiplying them but didn't because I thought it would give something horrible, very possibly with things being squared again (which obviously is not the objective of the question) but I will give it a go!

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(Original post by

Note that cos^4(theta) can be written as (1-sin^2(theta))^2

Maybe manipulation using this may help you express the integrand in terms of powers of sines and then you may be able to integrate term by term

**BrandonS15**)Note that cos^4(theta) can be written as (1-sin^2(theta))^2

Maybe manipulation using this may help you express the integrand in terms of powers of sines and then you may be able to integrate term by term

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#6

(Original post by

Thanks for that

Yeah, it does mean something to me.

I thought about multiplying them but didn't because I thought it would give something horrible, very possibly with things being squared again (which obviously is not the objective of the question) but I will give it a go!

**jamiet0185**)Thanks for that

Yeah, it does mean something to me.

I thought about multiplying them but didn't because I thought it would give something horrible, very possibly with things being squared again (which obviously is not the objective of the question) but I will give it a go!

https://www.wolframalpha.com/input/?...sin%5E3%28x%29

Last edited by mqb2766; 4 weeks ago

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(Original post by

Added link with some examples.

**mqb2766**)Added link with some examples.

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#8

(Original post by

Thank you

**jamiet0185**)Thank you

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#9

(Original post by

Ah, thanks for that, I'll give it a try!

**jamiet0185**)Ah, thanks for that, I'll give it a try!

If you're aiming to get to a sum of single trig functions, I'd use the (z+1/z)^4(z-1/z)^3 form, note that (z+1/z)(z-1/z) = (z^2 - 1/z^2) to rewrite as (z^2-1/z^2)^3 (z+1/z), and multiply out. It's not too bad. (It does feel there "should" be a slightly shorter way, but it's short enough to be fairly acceptable).

Incidentally, if we're talking about "not using de Moivre", it's worth noting that if you want to find

where n is

**odd**, then the fastest solution is almost certainly to rewrite the integrand as

. If you then expand out the integrand, you're left with a bunch of terms of form , which can be integrated by recognition as .

(This totally fails to work when n is even, unfortunately).

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Thanks everyone for the help.

Ignore the picture below

Ignore the picture below

Last edited by jamiet0185; 4 weeks ago

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I'm just not getting to the right answer. Can someone point out where I've gone wrong please?

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#12

When you "convert back" from your powers of z to sin/cos, you've gone from z^k -1/z^k to sin kz when you should have gone to 2i sin kz. (Not sure that's the only error - on mobile).

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(Original post by

When you "convert back" from your powers of z to sin/cos, you've gone from z^k -1/z^k to sin kz when you should have gone to 2i sin kz. (Not sure that's the only error - on mobile).

**DFranklin**)When you "convert back" from your powers of z to sin/cos, you've gone from z^k -1/z^k to sin kz when you should have gone to 2i sin kz. (Not sure that's the only error - on mobile).

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#14

**jamiet0185**)

Hi

Could anyone help me get started with this question please?

I understand how to do it for example with cos^5x or sin^3x but I'm not sure what to when they're multiplied together as in question 6 below...

Thanks in advance!

My hunch is that once you do that, you can proceed as per normal.

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#15

(Original post by

Have you tried the identity: cos^2 x = 1-sin^2 x?

My hunch is that once you do that, you can proceed as per normal.

**boulderingislife**)Have you tried the identity: cos^2 x = 1-sin^2 x?

My hunch is that once you do that, you can proceed as per normal.

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I'm really sorry but there's another bit I don't know how to approach. Could anyone suggest how to start Q8ii

Thanks again!!

Thanks again!!

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#17

Divide by cos t (which you're told is not zero). RHS is then a quadratic in cos^2 t.

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#18

(Original post by

I'm really sorry but there's another bit I don't know how to approach. Could anyone suggest how to start Q8ii

Thanks again!!

**jamiet0185**)I'm really sorry but there's another bit I don't know how to approach. Could anyone suggest how to start Q8ii

Thanks again!!

Should end up with something like:

t(t^2+k)(t^2+h) =0. Then you can solve for theta

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#19

(Original post by

Although it's a viable method, it's not the desired approach if you are supposed to use De Moivre's theorem.

**DFranklin**)Although it's a viable method, it's not the desired approach if you are supposed to use De Moivre's theorem.

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