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Math Help - Simplifying Trigonometric Equations

  1. #1
    sar
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    Simplifying Trigonometric Equations

    Hi all! I know this is probably a fairly simple concept for Trigonometry, but I can't quite remember how to do them. I'm just trying to make sure I know them well enough so that I can do them on a test I have in a few days. It would be awesome if you could just get me started on them.

    1. cot(x)sin(x) = \frac{\sqrt{3}}{2}

    2. tan(x) cos(x) = 1

    3. sin^2(x) + cos^2(x) + cos(x) = 1

    4. [ cot(x) (\frac{sin(x)}{cos(x)})] sec^2(x) = \frac{1}{2}
    Last edited by sar; February 23rd 2009 at 02:04 PM.
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  2. #2
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    Quote Originally Posted by sar View Post
    Hi all! I know this is probably a fairly simple concept for Trigonometry, but I can't quite remember how to do them. I'm just trying to make sure I know them well enough so that I can do them on a test I have in a few days. It would be awesome if you could just get me started on them.

    1. cot(x)sin(x) = \frac{\sqrt{3}}{2}
    It is normally best to write all of your sec(x), csc(x), tan(x), and cot(x) in terms of sin(x) and cos(x). That way, if anything cancels, you can simplify the expression.

    \frac{cos(x)}{sin(x)}  sin(x) = \frac{\sqrt{3}}{2}

    Hey, there's a sin(x) on the top as well as the bottom! So, as long as the sin(x) is not zero, we're ok to divide the top and bottom by sin(x) and cancel them.

    cos(x) = \frac{\sqrt{3}}{2}

    So which angles have a cosine value of \frac{\sqrt{3}}{2} ?

    Once you've deduced what x is, don't forget, you can't have any angles that would let sin(x) be equal to zero. So you'll have to examine your answers and refuse any answers that had a sin value of zero.
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  3. #3
    sar
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    Wow, that made it so much easier! Thanks a bunch!
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