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 Post subject: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:17:49 UTC
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Joined: Wed, 4 Apr 2012 20:15:46 UTC
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Am I on the right track for finding all solutions and find solutions in a set from [0,2pi)

csc 3x = 5 sin 3x

1/sin 3x = 5 sin 3x

1/5 = sin 3x^2

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:22:17 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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djsgarrett wrote:
Am I on the right track for finding all solutions and find solutions in a set from [0,2pi)

csc 3x = 5 sin 3x

1/sin 3x = 5 sin 3x

1/5 = sin 3x^2

OK, now finish it...

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:31:43 UTC
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Joined: Wed, 4 Apr 2012 20:15:46 UTC
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sin 3x^2 = 1/5

sin 3x = sqrt(1/5)

sin x = (1/3)(sqrt 1/5)

I think I got the rest!

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:38:57 UTC
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djsgarrett wrote:
sin 3x^2 = 1/5

sin 3x = sqrt(1/5)

sin x = (1/3)(sqrt 1/5)

I think I got the rest!

NO!

1. Remember there are two square roots of 1/5
2. You cannot just bring the 3 out, you have to take the arcsine first.

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:45:29 UTC
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Joined: Wed, 4 Apr 2012 20:15:46 UTC
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sin 3x = +/- sqrt(1/5)

x = (1/3)[sin^-1(+/-sqrt(1/5)) + 2k*pi] or x = (1/3)[pi -sin^-1(+/-sqrt(1/5)) + 2k*pi]

I left out the +/- earlier and was finishing up when I saw your post. I think I have it.

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:48:12 UTC
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djsgarrett wrote:
sin 3x = +/- sqrt(1/5)

x = (1/3)[sin^-1(+/-sqrt(1/5)) + 2k*pi] or x = (1/3)[pi -sin^-1(+/-sqrt(1/5)) + 2k*pi]

I left out the +/- earlier and was finishing up when I saw your post. I think I have it.

Yes. Well done!

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:52:58 UTC
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Joined: Wed, 4 Apr 2012 20:15:46 UTC
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Thanks! Sometimes I just need to pointed in the right direction, my compass does not always work!

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 Post subject: Re: Csc 3x = 5 sin 3xPosted: Thu, 5 Apr 2012 03:55:24 UTC
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djsgarrett wrote:
Thanks! Sometimes I just need to pointed in the right direction, my compass does not always work!

That's fine, and we're glad to help. But be sure to post what work you have as a general rule, otherwise you run the risk of having your posts deleted.

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