Answer
$7.67^{\circ}$
Work Step by Step
Ensuring that the calculator is in degree mode, we enter $\csc^{-1} (7.4890096)$ as $\sin^{-1} (\frac{1}{7.4890096})$ into the calculator and solve:
$\sin^{-1} (\frac{1}{7.4890096})\approx7.67^{\circ}$
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