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Math Help - Determining the exact value of each expression

  1. #1
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    Determining the exact value of each expression

    Hi guys, I'm having trouble with obtaining the correct results for this expression.

    The question is: Determine the exact value of each expression.

    [cos(pi/4)tan(5pi/6)] / [sin(3pi/4)]

    Somehow, I obtained the answer square root of three... but the answer is supposed to be square root of 6 divided by 6.

    Thank you in advance for all of your help.
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  2. #2
    Member Henderson's Avatar
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    Are you sure either answer is right, or that you copied the problem correctly?

    I get an answer of -\frac{\sqrt3}{3}.

    \frac{(\frac{\sqrt2}{2})\cdot(-\frac{\sqrt3}{3})}{(\frac{\sqrt2}{2})}
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  3. #3
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Henderson View Post
    Are you sure either answer is right, or that you copied the problem correctly?

    I get an answer of -\frac{\sqrt3}{3}.

    \frac{(\frac{\sqrt2}{2})\cdot(-\frac{\sqrt3}{3})}{(\frac{\sqrt2}{2})}
    Ditto what Henderson said
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  4. #4
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    Oh no! I didn't copy it right! It's supposed to be cos(4pi/3) instead of cos(pi/4)
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  5. #5
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    well, you should know that \cos\left(\frac{4\pi}{3}\right) = -\frac{1}{2}

    sub it in for the \frac{\sqrt{2}}{2} in the numerator of the expressions given and re-evaluate.
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  6. #6
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    how did you get square root of 2 over 2 as the denominator tho?

    -cos(pi/3) = -1/2
    -tan(pi/6) = - 1/ square root of 3
    sin(pi/4) = 1/ square root of 2
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  7. #7
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    \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}
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  8. #8
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    i mean.. how did you get your answer? the answer that i got wat 2/(2*square root of 3)
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