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Math Help - Inverse Trigonometric Functions

  1. #1
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    Inverse Trigonometric Functions

    y= arcsin x
    Find the right end behavior model, the left hand behavior model, and any horizontal tangents for the function if they exist.

    The tangent I can find easily with a calculator, but the behaviors I don't know.

    I also need to do it for arccos x, though I think I should be able to get it after knowing arcsin x.
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  2. #2
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    Quote Originally Posted by Truthbetold View Post
    y= arcsin x
    Find the right end behavior model, the left hand behavior model, and any horizontal tangents for the function if they exist.

    The tangent I can find easily with a calculator, but the behaviors I don't know.

    I also need to do it for arccos x, though I think I should be able to get it after knowing arcsin x.
    Hello,

    only functions with unchanging monotony (I know that this expression is not appropriate - I mean the first derivative is allways positive or allways negative) have inverse functions. The sin-function has to be bounded to be monotonously increasing (or decreasing). Usually you take the interval \left [-\frac{\pi}{2}, \frac{\pi}{2}\right ].
    Thus you have:

    \begin{array}{l}x\mapsto \sin(x), \ \left [-\frac{\pi}{2}, \frac{\pi}{2}\right ] \mapsto [-1, 1] \\ \ \\x\mapsto \arcsin(x), \ [-1, 1] \mapsto \left [-\frac{\pi}{2}, \frac{\pi}{2}\right ] \end{array}

    Therefore examine the arcsin-function if x appraches -1 from the right and when x approaches +1 from the left.
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  3. #3
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    So the right is -pi/2 - because the limit as x--> -1 from the right is -pi/2
    and the left is pi/2- because the limit as x--> 1 from the left is pi/2.
    The answer is pi/2 for both.

    What I did I do wrong?
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