12. Find the measure(s) of $\mathrm{A}$, to the nearest degree, where $0^{\circ} \leq A \leq 360^{\circ}$. a) $\sin A=-0.9580$ b) $\tan A=\frac{5}{2}$ c) $\csc A=1.0138$

Step 1 ：The sine function is negative in the third and fourth quadrants.

Step 2 ：We can use the arcsin function to find the reference angle, which is approximately \(73.34^{\circ}\).

Step 3 ：Then, subtract the reference angle from 180 degrees for the third quadrant to get \(253.34^{\circ}\).

Step 4 ：Subtract the reference angle from 360 degrees for the fourth quadrant to get \(286.66^{\circ}\).

Step 5 ：Rounding to the nearest degree, we get \(253^{\circ}\) and \(287^{\circ}\).

Step 6 ：Final Answer: The measures of \(A\), to the nearest degree, where \(0^{\circ} \leq A \leq 360^{\circ}\) and \(\sin A=-0.9580\) are approximately \(\boxed{253^{\circ}}\) and \(\boxed{287^{\circ}}\).