Find the sign of the following.
-$\csc ( - \theta )$, given that $\theta$ is in the interval $\left( 90 ^ { \circ } , 180 ^ { \circ } \right)$.
A) positive
B) negative

Question

Quizplus · Accepted Answer

The cosecant function, $\csc(\theta)$, is the reciprocal of the sine function. For angles in the interval $90^\circ < \theta < 180^\circ$, sine is positive because these angles fall in the second quadrant where sine values are positive. However, since the angle is negative $(- \theta)$, it reflects the angle to the fourth quadrant where sine values are negative. Since $\csc(\theta) = 1/\sin(\theta)$, $\csc(-\theta)$ will also be negative due to the negative sine value in the fourth quadrant.

Find the Sign of the Following csc⁡(−θ)\csc ( - \theta )csc(−θ)

Find the Sign of the Following $\csc ( - \theta )$