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Math Help - help with this trig identity problem

  1. #1
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    help with this trig identity problem

    Hi all again!

    Hoping you can help me with this one as I dont really have a clue how to go about it properly:

    2sin^2 x + 3cos x-3=0

    Ive used all kinds of identities and get really long and nonsensical answers, if someone could take me through step by step that would be ideal;
    I have the answer, I just need to know how to arrive at it!

    Thanks in advance!

    Rhys.
    Last edited by Rhys101; November 9th 2012 at 02:57 PM.
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  2. #2
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    Re: help with this trig identity problem

    \sin^2 x = 1 - \cos^2 x

    2(1 - \cos^2 x) + 3 \cos x - 3 = 0

    -2 \cos^2 x + 3 \cos x - 1 = 0

    Can you go from there?
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  3. #3
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    Re: help with this trig identity problem

    Wow, that was fast!
    Thanks, umm no not really, should I use the power reducing formula for the -2cos^2x or ignore it and use the sum to product formula on the whole thing? I am not sure.
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  4. #4
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    Re: help with this trig identity problem

    Quote Originally Posted by Rhys101 View Post
    Wow, that was fast!
    Thanks, umm no not really, should I use the power reducing formula for the -2cos^2x or ignore it and use the sum to product formula on the whole thing? I am not sure.
    You don't need any more trig identities from here. In fact, reducing \cos^2 x to \frac{1 + \cos 2x}{2} makes it even worse because you have a cos 2x and cos x in the same equation. Basically, the question can now be solved using just algebra. Do you see how?
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  5. #5
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    Re: help with this trig identity problem

    Of course! I am so dense! It's a quadratic, so I just use the quadratic formula to find cos x, yes? Will other other questions be similar to this? With the use of only one trig identity and doing the rest via algebra? Is it likely that with most equations I first have to make all the trig values the same so I can use them as a variable?
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  6. #6
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    Re: help with this trig identity problem

    or should i factor?
    Also: I cant find the trig identity that you used anywhere, the  sin^2 x= 1-cos^2 x would you be able to find me a link where this one is stashed? There might be others there I am missing and don't know about.

    Thanks again
    Last edited by Rhys101; November 9th 2012 at 08:38 PM.
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  7. #7
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    Re: help with this trig identity problem

    Ah, so is it the sinx = sqrt*(1-cos^2 x) but because of the power of 2 on the sin it cancels the square root? Also I factored and came up with the right answer
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  8. #8
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    Re: help with this trig identity problem

    Quote Originally Posted by Rhys101 View Post
    Ah, so is it the sinx = sqrt*(1-cos^2 x) but because of the power of 2 on the sin it cancels the square root? Also I factored and came up with the right answer
    Careful, \sin x might not equal \sqrt{1 - \cos^2 x}. It could equal -\sqrt{1 - \cos^2 x}. Better to leave it as sin^2 x.

    Great job with the correct answer.
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