Decide whether the statement is possible or impossible for an angle $\theta .$
-$\sin \theta = 0.7 \text { and } \csc \theta = - 0.7$
A) Impossible
B) Possible

Question

Quizplus · Accepted Answer

The sine and cosecant functions are reciprocal to each other, meaning $\csc \theta = \frac{1}{\sin \theta}$. If $\sin \theta = 0.7$, then $\csc \theta$ must be $\frac{1}{0.7}$, not $-0.7$. Therefore, it's impossible for $\sin \theta = 0.7$ and $\csc \theta = -0.7$ simultaneously.

Decide Whether the Statement Is Possible or Impossible for an Angle