- #1

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18sinxcosx=1-6sinx

Would there be an easy way other than trial and error?

Thanks

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- Thread starter O garcia
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- #1

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18sinxcosx=1-6sinx

Would there be an easy way other than trial and error?

Thanks

- #2

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Rather than just try solutions one by one, you could plot f(x) = 1 - 6 sin x - 9 sin 2x and locate the zeroes of the curve. There are four solutions in the interval [0, 2·pi]. The good news is that the function has a period of 2·(pi), so once you find those four, you can describe all the rest.

- #3

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scrap this

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- #4

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- #5

Science Advisor

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- #6

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By trigonometric sine rule, sin(a)cos(b)=(1/2)[sin(a+b)+sin(a-b)]

Edit: sorry, I'll use a and b to avoid confusion. Since a=b=x, then

Simplify this equation, we get (1/2)[sin(2x)+sin(x-x)]=sin(2x)/2 (*)

Plug (*) into the LHS, then we get 9sin(x)=1-6sin(x)

Solve, for x. It should be easy from here. =]

Edit: sorry, I'll use a and b to avoid confusion. Since a=b=x, then

Simplify this equation, we get (1/2)[sin(2x)+sin(x-x)]=sin(2x)/2 (*)

Plug (*) into the LHS, then we get 9sin(x)=1-6sin(x)

Solve, for x. It should be easy from here. =]

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- #7

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Hmm..I posted something similar to that but deleted it since I set the coefficient of -a*sin(x) to 1 instead of 6.

One thing to note though, if you fling this into a CAS...you get a very, ahem... 'clever looking' solution. (ie; ridiculously messy!) :tongue2:

- #8

Homework Helper

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By trigonometric sine rule, sin(x)cos(x)=(1/2)[sin(x+x)+sin(a-x)]

Simplify this equation, we get (1/2)[sin(2x)+sin(x-x)]=sin(2x)/2 (*)

Plug (*) into the LHS, then we get 9sin(x)=1-6sin(x)

Solve, for x. It should be easy from here. =]

You dropped a '2' in that last equation: that should be

9 sin(

which is what I gave back in post #2. Unfortunately, there isn't any

Alas, I looked at that possibility and it doesn't work for this equation. An approach of that sort will work for certain special cases of the numerical coefficients -- but this ain't one o'them...

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- #9

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Ah, sorry. I didn't see that.You dropped a '2' in that last equation: that should be

9 sin(2x) = 1 - 6 sin(x) ,

which is what I gave back in post #2. Unfortunately, there isn't anyniceway to solve that...

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