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# Trigonometry question watch

1. If

Find:
2. Just an idea. It looks like a GP with first term and ratio
If

Find:

Are you sure you don't mean

Find:

4. By magic I have the angle to be 0.574826 radians and the value of the required expression to be 7.96946

I think the answer should be 8
5. cos^6-4cos^4+8cos^2 gives a nice answer.
cos^6+4cos^4+8cos^2 = 7.969460322719865 to 15 d.p. and that answer has no match on the inverse symbolic calculator (so it's unlikely there's a very 'nice' form for it's value).
6. (Original post by steve2005)
Just an idea. It looks like a GP with first term and ratio
A very good point, which means that S^4 = 2S -1 (S = SINX)

If C = COSX , then the thing can be factorised as C^2(C^4 - 4C^2 + 8)

C^4- 4C^2 + 8 = (C^2 - 2 )^2 + 4

After which it is 'simply' a case of using cos squared + sin Squared = 1, and replacing all Sin to the power 4 with 2 Sin - 1. That gets you the odd powers of sin which you eliminate as S + S squared + S cubed = 1
7. Nevermind. hahaha i screwed up hard. >.<

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Updated: August 10, 2009
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