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How many possible values for y are there where y = cos^-1 0?
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If you mean \[y= \cos^{-1}(0) \] then are infinitly many of them. Like \[ \pm \frac \pi 2 + 2 k \pi, k=0,\pm 1, \pm 2, .... \]
hell no
arccosine is a well defined function one input one output \[\cos^{-1}(0)=\frac{\pi}{2}\] and no other number
I agree with you if you restrict the domain to get a function. But there are infinite values x so that cos(x)=0
and i agree with you that there are infinitely many x such that \(\cos(x)=0\) however there is only one \(\cos^{-1}(0)\)
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Depending how you define the question.
In some books Arccos is the one valued function and \[ \cos^{-1} \] is the multivalued function.
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