Answer
$x = arcsin(\frac{5}{4}~y+\frac{3}{4})$
Work Step by Step
$y = \frac{4}{5}~sin~x-\frac{3}{5}$
$\frac{4}{5}~sin~x = y+\frac{3}{5}$
$sin~x = \frac{5}{4}(y+\frac{3}{5})$
$x = arcsin(\frac{5}{4}~y+\frac{3}{4})$
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