1. The problem is to evaluate $\csc 270^\circ$ without using a calculator. 2. Recall that $\csc \theta = \frac{1}{\sin \theta}$, so we need to find $\sin 270^\circ$ first. 3. The angle $270^\circ$ corresponds to the point on the unit circle at the negative y-axis, where $\sin 270^\circ = -1$. 4. Using the formula, $\csc 270^\circ = \frac{1}{\sin 270^\circ} = \frac{1}{-1} = -1$. 5. Therefore, the value of $\csc 270^\circ$ is $-1$.