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

Question

Quizplus · Accepted Answer

The csc of an angle θ, given a point $(-2, -1)$ on its terminal side, is the reciprocal of the sine. The sine is calculated as $y/r$, where $r = \sqrt{x^2 + y^2}$. Here, $r = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5}$, so $\sin \theta = -1/\sqrt{5}$ and $\csc \theta = -\sqrt{5}$.

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