Provide an appropriate response.
-Find $\cot \theta$, given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.
A) $\frac { 3 \sqrt { 7 } } { 7 }$
B) $\frac { 5 } { 4 }$
C) $- \frac { 3 } { 2 }$
D) $- \frac { \sqrt { 7 } } { 9 }$

Question

Quizplus · Accepted Answer

$\cot \theta = \frac{1}{\tan \theta}$, so given $\tan \theta = \frac{\sqrt{7}}{3}$, $\cot \theta = \frac{3}{\sqrt{7}}$. To rationalize, multiply numerator and denominator by $\sqrt{7}$, resulting in $\frac{3\sqrt{7}}{7}$. Since $\theta$ is in quadrant III, both $\tan \theta$ and $\cot \theta$ should be positive, but the question implies a misunderstanding of the trigonometric function signs in quadrant III. Despite this, based on the calculation, option A is the correct transformation of the given $\tan \theta$ to $\cot \theta$.

Provide an Appropriate Response cot⁡θ\cot \thetacotθ , Given That tan⁡θ=73\tan \theta = \frac { \sqrt { 7 } } { 3 }tanθ=37​​

Provide an Appropriate Response $\cot \theta$ , Given That $\tan \theta = \frac { \sqrt { 7 } } { 3 }$