Evaluate without using a calculator by using ratios in a reference triangle.
-$\csc 45 ^ { \circ }$
A) $\sqrt { 2 }$
B) $\sqrt { 3 }$
C) $\frac { \sqrt { 2 } } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

The cosecant function is the reciprocal of the sine function. For a 45-degree angle in a right triangle, $\sin 45^\circ = \frac{\sqrt{2}}{2}$, so $\csc 45^\circ = \frac{1}{\sin 45^\circ} = \sqrt{2}$.

Evaluate Without Using a Calculator by Using Ratios in a Reference