Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\csc 45 ^ { \circ }$
A) 1
B) $\sqrt { 2 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 2 \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The cosecant of an angle is the reciprocal of the sine of that angle. For $45^\circ$, $\sin 45^\circ = \frac{\sqrt{2}}{2}$, so $\csc 45^\circ = \frac{1}{\sin 45^\circ} = \frac{2}{\sqrt{2}} = \sqrt{2}$.

Without Using a Calculator, Give the Exact Trigonometric Function Value csc⁡45∘\csc 45 ^ { \circ }csc45∘

Without Using a Calculator, Give the Exact Trigonometric Function Value $\csc 45 ^ { \circ }$