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\section{Complex values}{
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\section{Complex values}{
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For the inverse trigonometric functions, branch cuts are defined as in
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For the inverse trigonometric functions, branch cuts are defined as in
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\bibcitet{|R:Abramowitz+Stegun:1972|figure 4.4 on page 79}.
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\bibcitet{|R:Abramowitz+Stegun:1972|figure 4.4 on page 79}.
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For \code{asin} and \code{acos}, there are two cuts, both along
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For \code{asin} and \code{acos}, there are two cuts, both along
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the real axis: \eqn{\left(-\infty, -1\right]}{(-Inf, -1]} and
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the real axis: \eqn{\left(-\infty, -1\right]} and
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\eqn{\left[1, \infty\right)}{[1, Inf)}.
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\eqn{\left[1, \infty\right)}.
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For \code{atan} there are two cuts, both along the pure imaginary
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For \code{atan} there are two cuts, both along the pure imaginary
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axis: \eqn{\left(-\infty i, -1i\right]}{(-1i*Inf, -1i]} and
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axis: \eqn{\left(-\infty i, -1i\right]}{(-1i*Inf, -1i]} and
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\eqn{\left[1i, \infty i\right)}{[1i, 1i*Inf)}.
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\eqn{\left[1i, \infty i\right)}{[1i, 1i*Inf)}.
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