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[H]manipulating trigonometric identities

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Heggie United Kingdom167 Posts May 04 2009 14:13 GMT #1 I need to manipulate 2sin3xsin2x into a form I can integrate. The mark scheme says you have to manipulate it to cosx-cos5x before you can integragte but does not elaborate on how! Could someone give me a clue as to what trigonometric identities I should be using here? Major thanks to anyone who can help. peace

Plutonium United States2217 Posts May 04 2009 14:48 GMT #2 To get from the first to the second, you have to use the Product Formula: sin(x)sin(y) = [cos(x - y) - cos(x + y)] / 2 Though I'm not sure why you can't just integrate the first form.

Heggie United Kingdom167 Posts May 04 2009 15:24 GMT #3 Nice one Plutonium. How would you integrate in the first form out of interest?

Plutonium United States2217 Posts May 04 2009 16:10 GMT #4 Hell if I remember. I just searched google for trig identities. It probably involves U-V integration though.

Wohmfg United Kingdom1292 Posts May 04 2009 16:25 GMT #5 Yeah, to integrate a product of functions you have to do integration by parts (using u and v as your functions). I dunno if you've covered that yet but I guess you don't need it anyway :D

Heggie United Kingdom167 Posts May 04 2009 16:52 GMT #6 Yeah I have mate, but I'm not sure it is useful here. No matter how many times you apply it I don't think it will make either of the xs "disappear", so you will still have a product of two functions of x in the integral you subtract.

Wohmfg United Kingdom1292 Posts May 04 2009 17:11 GMT #7 Ah yes my bad, of course you can't do that with trigonometric functions.

KlaCkoN Sweden1661 Posts May 04 2009 18:03 GMT #8 Why yes, it is possible to do it by parts. It is absolutely retarded in this case but it is possible. (Do it twice you get the original primitive back but multiplied by a constant, solve for it algebraically.)

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