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Math Help - How do you simplify this problem?

  1. #1
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    How do you simplify this problem?

    sin(\frac{-3pi}{4}) cos(\frac{5pi}{6})



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  2. #2
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    Quote Originally Posted by Darkhrse99 View Post
    sin(\frac{-3pi}{4}) cos(\frac{5pi}{6})
    Didn't I tell you before to memorize certain trigonometric values? It seems you have not fulfilled this assignment.

    sin(-3pi/4) = -sin(3pi/4) = -sin(pi/4) = ???

    cos(5pi/6) = -cos(pi/6) = ???

    Now what?

    Note: If you're using LaTeX, feel free to put a slash in front of those "pi"s. Excellent results can be obtained.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Didn't I tell you before to memorize certain trigonometric values? It seems you have not fulfilled this assignment.

    sin(-3pi/4) = -sin(3pi/4) = -sin(pi/4) = ??? \frac{\sqrt1}{2}?

    cos(5pi/6) = -cos(pi/6) = ??? \frac{1}{2}?

    Now what?

    Note: If you're using LaTeX, feel free to put a slash in front of those "pi"s. Excellent results can be obtained.
    Is this correct?
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  4. #4
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    Sorry, it's a little like you are just throwing darts.

    On the first:

    1) Where did the negative sign go?

    2) \sqrt{1}?

    On the second:

    3) Where did the negative sign go?

    4) Please note the difference between \frac{\pi}{6} and \frac{\pi}{3}.

    Look at a chart of values. Think it through. Don't just stab at it.
    Last edited by TKHunny; June 19th 2008 at 04:51 AM.
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  5. #5
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    So the first on is  \frac{-\sqrt1}{2} and the second one is.  \frac{-\sqrt3} {2}. I'm finding the (-)(Y value for \frac{\pi}{4}
    and the X value for \frac{\pi}{4} Is this correct. I'm not trying to take stabs at it, but i truely don't know how to do the problem.
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  6. #6
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    Is this answer correct?
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  7. #7
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    You must MEMORIZE a few important values.

    0\;\;\sin(0)\;=\;0\;\;\cos(0)\;=\;1

    \frac{\pi}{6}\;\;\sin(\frac{\pi}{6})\;=\;\frac{1}{  2}\;\;\cos(\frac{\pi}{6})\;=\;\frac{\sqrt{3}}{2}

    \frac{\pi}{4}\;\;\sin(\frac{\pi}{4})\;=\;\frac{\sq  rt{2}}{2}\;\;\cos(\frac{\pi}{4})\;=\;\frac{\sqrt{2  }}{2}

    \frac{\pi}{3}\;\;\sin(\frac{\pi}{3})\;=\;\frac{\sq  rt{3}}{2}\;\;\cos(\frac{\pi}{3})\;=\;\frac{1}{2}

    \frac{\pi}{2}\;\;\sin(\frac{\pi}{2})\;=\;1\;\;\cos  (\frac{\pi}{2})\;=\;0

    There is NO substitute for memorizing this tableau. Put it in your brain.

    Note: You still have \sqrt{1}. Don't write things that make no sense.
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  8. #8
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    Thanks for the help.

    My text book shows that  \frac{\sqrt1}{2} is the same as \frac{\sqrt2}{2}
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  9. #9
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    So really what I'm trying to do when simplifying is getting the x or y of the above table?


    So in the problem below I need to find the X or Y value?
    Simplify  tan(\frac{-2\pi}{3})csc(\frac{3\pi}{4})
    Tan= \frac{Y}{X} CSC= \frac{1}{Y} Do I find the x or y value for tan and cosecant?
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  10. #10
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    Quote Originally Posted by Darkhrse99 View Post
    Thanks for the help.

    My text book shows that  \frac{\sqrt1}{2} is the same as \frac{\sqrt2}{2}
    No, once again, it's not \frac{\sqrt1}{2} but \sqrt{\frac 12} which is the same as \frac{\sqrt2}{2}
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  11. #11
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    or maybe \frac{1}{\sqrt{2}}.

    Notation means stuff. Don't disregard it for expediency.
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  12. #12
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    Quote Originally Posted by Darkhrse99 View Post
    So really what I'm trying to do when simplifying is getting the x or y of the above table?


    So in the problem below I need to find the X or Y value?
    Simplify  tan(\frac{-2\pi}{3})csc(\frac{3\pi}{4})
    Tan= \frac{Y}{X} CSC= \frac{1}{Y} Do I find the x or y value for tan and cosecant?
    What does your memorized table tell you?
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