Use the given values to evaluate (if possible) three trigonometric functions $\operatorname { cosec } \theta$ $\tan \theta , \cos \theta$ $\sin \theta = - 3 , \quad \cot \theta = 0$
A) $\csc \theta = - \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = - 2 \sqrt { 2 }$
B) $\csc \theta = - \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = 0$
C) $\csc \theta = \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = - 2 \sqrt { 2 }$
D) $\csc \theta = \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = 2 \sqrt { 2 }$
E) $\csc \theta$ is undefined.
$\tan \theta = \frac { 1 } { 3 }$
$\cos \theta = - 2 \sqrt { 2 }$

Question

Use the given values to evaluate (if possible) three trigonometric functions $\operatorname { cosec } \theta$ $\tan \theta , \cos \theta$ $\sin \theta = - 3 , \quad \cot \theta = 0$ 
A) $\csc \theta = - \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = - 2 \sqrt { 2 }$
B) $\csc \theta = - \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = 0$
C) $\csc \theta = \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = - 2 \sqrt { 2 }$
D) $\csc \theta = \frac { 1 } { 3 }$
$\tan \theta$ is undefined.
$\cos \theta = 2 \sqrt { 2 }$
E) $\csc \theta$ is undefined.
$\tan \theta = \frac { 1 } { 3 }$
$\cos \theta = - 2 \sqrt { 2 }$

Quizplus · Accepted Answer

We know that $\csc 	heta$ is the reciprocal of $\sin 	heta$, which is given as $-3$. Therefore, $\csc 	heta = - \frac{1}{3}$. We also know that $\cot 	heta = \frac{1}{	an 	heta}$, which is given as $0$. Therefore, $	an 	heta$ is undefined. Finally, using the Pythagorean identity $\sin^2 	heta + \cos^2 	heta = 1$, we can solve for $\cos 	heta$ as $0$. Therefore, the best choice is B.

Use the Given Values to Evaluate (If Possible) Three Trigonometric cosec⁡θ\operatorname { cosec } \thetacosecθ

Use the Given Values to Evaluate (If Possible) Three Trigonometric $\operatorname { cosec } \theta$