Answer
1.0210339
Work Step by Step
Step 1: First, we convert the angle in decimal degrees:
$78^{\circ}21'=78\frac{21}{60}^{\circ}=78.35^{\circ}$
Therefore, $\csc 78^{\circ}21'=\csc 78.35^{\circ}$.
Step 2: Using the reciprocal identity $\csc\theta=\frac{1}{\sin\theta}$,
$\csc 78.35=\frac{1}{\sin 78.35}$
Step 3: Now, we check to ensure that the calculator is in degree mode.
Step 4: We then type $\frac{1}{\sin 78.35}$ into the calculator.
Step 5: Solving, $\frac{1}{\sin 78.35}\approx1.0210339$.
