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Math Help - Evaluate without calculator

  1. #1
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    Evaluate without calculator

    Help please. Sorry if Im posting several threads. I have an examination tomorrow and need to know how to solve this.

    1. cot [{Arcsec (-2 \sqrt{3/4}) }]

    2. sin [{arctan (\frac{-5}{12}) }]

    3. Cos^{-1}[{1/2\sqrt{2}   cos[Sin^{-1} (-1) }]
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  2. #2
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    Quote Originally Posted by reiward View Post
    Help please. Sorry if Im posting several threads. I have an examination tomorrow and need to know how to solve this.

    1. cot [{Arcsec (-2 \sqrt{3/4}) }]

    2. sin [{arctan (\frac{-5}{12}) }]

    3. Cos^{-1}[{1/2\sqrt{2} cos[Sin^{-1} (-1) }]
    I will do 1. The others follow a similar approach.

    Let \text{arcsec} (- \sqrt{3}) = \alpha \Rightarrow \sec \alpha = - \sqrt{3} (think carefully about what quadrant \alpha is in).

    Knowing \sec \alpha = - \sqrt{3} you should be able to calculate \cot \alpha.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    I will do 1. The others follow a similar approach.

    Let \text{arcsec} (- \sqrt{3}) = \alpha \Rightarrow \sec \alpha = - \sqrt{3} (think carefully about what quadrant \alpha is in).

    Knowing \sec \alpha = - \sqrt{3} you should be able to calculate \cot \alpha.
    Oh okay. So I need to draw the graph.

    Uhm. Can you help me on the last number? I'm clueless
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  4. #4
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    Quote Originally Posted by reiward View Post
    Oh okay. So I need to draw the graph.

    Uhm. Can you help me on the last number? I'm clueless
    Perhaps start with the fact that \sin^{-1} (-1) = - \frac{\pi}{2} ....
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