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        The Pythagorean trigonometric identity is given by
        \begin{equation} \sin^2(\theta) + \cos^2(\theta) = 1. \end{equation}
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    of
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    \begin{equation*}
        \begin{split}
        A & = \frac{\pi r^2}{2} \\
         & = \frac{1}{2} \pi r^2
        \end{split}
    \end{equation*}
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