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Math Help - inverse trig

  1. #1
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    inverse trig

    (theta) = cos ^-1(x) double arrow x=cos(theta) Is this a true or false statement and if so how can I verify it?
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  2. #2
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    \theta = \cos^{-1} x \: \: \Rightarrow \: \: \cos \theta = x

    But not the other way around: \cos \theta = x \: \: \not{\Rightarrow} \: \: \theta = \cos^{-1} x strictly speaking in the sense that the inverse cosine function has a range of [0, \pi]


    For example, \theta = \frac{5\pi}{4} \: , \: x = -\frac{\sqrt{2}}{2}

    \cos \left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}

    But: \cos^{-1} \left(-\frac{\sqrt{2}}{2}\right) = \frac{3\pi}{4}
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