Answer
$5.999827^{\circ}$
Work Step by Step
Step 1: Using the reciprocal identity $\csc\theta=\frac{1}{\sin\theta}$, we write $\csc \theta=9.5670466$ as $\frac{1}{\sin\theta}=9.5670466$
Step 2: Using cross-multiplication,
$\frac{1}{\sin\theta}=\frac{9.5670466}{1}$ is written as $\sin\theta=\frac{1}{9.5670466}$
Step 3: Writing $\sin\theta=\frac{1}{9.5670466}$ as $\theta=\sin^{-1} \frac{1}{9.5670466}$
Step 4: Using degree mode, we type $\sin^{-1} \frac{1}{9.5670466}$ into the calculator and solve:
$\theta=\sin^{-1} \frac{1}{9.5670466}=5.999827^{\circ}$
