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Math Help - inverse trig functions

  1. #1
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    inverse trig functions

    how can I simplify this: tan(arcsin(x))
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  2. #2
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    Hello, xxju1anxx!

    Simplify: . \tan\bigg[\arcsin(x)\bigg]
    An inverse trig function is an angle.

    Let \theta \,=\,\arcsin(x) \quad\Rightarrow\quad\sin\theta \,=\,x

    We have: . \sin\theta \:=\:\frac{x}{1} \:=\:\frac{opp}{hyp}

    \theta is in a right triangle with: . opp = x,\;hyp = 1
    . . Using Pythagorus, we find that: . adj = \sqrt{1-x^2}
    Hence: . \tan\theta \:=\:\frac{opp}{adj} \:=\:\frac{x}{\sqrt{1-x^2}}

    Therefore: . \tan\bigg[\arcsin(x)\bigg] \;=\;\tan(\theta) \;=\;\frac{x}{\sqrt{1-x^2}}

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