A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( - 2 , - 1 ) \quad$ Find $\csc \theta .$
A) $- 5$
B) $- \sqrt { 5 }$
C) $\sqrt { 5 }$
D) $- 2$

Question

Quizplus · Accepted Answer

The csc of an angle is the reciprocal of the sine, which is opposite over hypotenuse. For a point (-2, -1), the hypotenuse is $\sqrt{(-2)^2 + (-1)^2} = \sqrt{5}$, and the sine is opposite/hypotenuse = -1/$\sqrt{5}$. Thus, $\csc \theta = 1/\sin \theta = -\sqrt{5}$.

A Point on the Terminal Side of an Angle θ (−2,−1)( - 2 , - 1 ) \quad(−2,−1)

A Point on the Terminal Side of an Angle θ $( - 2 , - 1 ) \quad$