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pure 5 ---Complex number HELP!!!!!!!!!!!!!!!!!!!!

Express the following in the terms of multiple angles.
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Reply 1
Avatar for theone
theone
Have you tried expressing both sin^3 and cos^4 in terms of multiples of sin x and cos x, sin 2x, cos 2x, etc... respectively?
Reply 2
Avatar for Werther
Werther
5
If you change everything to powers of cos first, then you can use De Moivre to express these as cosines of multiples of theta, and add the results together.

I don't know if it will work by using both sin and cos, as you'd end up with terms in sin3x.cos4x, I think, which isn't as neat.

My solution's pretty lengthy - I don't know if they'd set this question in an exam (as you say P5, not P6, I assume you're not doing the Edexcel syllabus), as it's fairly repetetive. There might be a faster way, though.
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Reply 3
Avatar for superkillball
superkillball
OP
1
Werther
If you change everything to powers of cos first, then you can use De Moivre to express these as cosines of multiples of theta, and add the results together.

I don't know if it will work by using both sin and cos, as you'd end up with terms in sin3x.cos4x, I think, which isn't as neat.

My solution's pretty lengthy - I don't know if they'd set this question in an exam (as you say P5, not P6, I assume you're not doing the Edexcel syllabus), as it's fairly repetetive. There might be a faster way, though.


Thank you very much.

ps: I am doing OCR MEI.

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