11. If $\cos A=-0.28$, where $\pi \leq A \leq \frac{3 \pi}{2}$, determine the exact value of $\csc A$.

Step 1 ：We are given that \(\cos A = -0.28\) and \(\pi \leq A \leq \frac{3 \pi}{2}\).

Step 2 ：We know that \(\sin^2 A + \cos^2 A = 1\). We can use this identity to find the sine of the angle.

Step 3 ：Since the angle is in the third quadrant, the sine of the angle will be negative.

Step 4 ：By substituting the given value of \(\cos A\) into the identity, we find that \(\sin A = -0.96\).

Step 5 ：The cosecant of an angle is the reciprocal of the sine of the angle. So, \(\csc A = -1.0416666666666667\).

Step 6 ：Final Answer: The exact value of \(\csc A\) is \(\boxed{-1.0416666666666667}\).