Word Count : 349

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Let ( \omega = \sin z ), where ( z = x + iy ) and ( \omega = u + iv ) with ( u(x,y) ) and ( v(x,y) ) real functions. Then [ \sin z = \sin(x + iy) = \sin x \cosh y + i \cos x \sinh y. ] So, [ u(x,y) = \sin x \cosh y, \quad v(x,y) = \cos x \sinh y. ] ____ _____ ___ _________ ______ ___ ____ ____.
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