Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\tan \theta$, if $\cot \theta = \frac { \sqrt { 7 } } { 3 }$
A) $\frac { 3 \sqrt { 7 } } { 7 }$
B) $\frac { \sqrt { 7 } } { 7 }$
C) $\frac { \sqrt { 3 } } { 7 }$
D) $\frac { 7 \sqrt { 7 } } { 3 }$

Question

Quizplus · Accepted Answer

The reciprocal identity of $\cot \theta$ is $\tan \theta = \frac{1}{\cot \theta}$, so $\tan \theta = \frac{1}{\frac{\sqrt{7}}{3}} = \frac{3}{\sqrt{7}}$, which rationalizes to $\frac{3\sqrt{7}}{7}$.

Use the Appropriate Reciprocal Identity to Find the Function Value tan⁡θ\tan \thetatanθ

Use the Appropriate Reciprocal Identity to Find the Function Value $\tan \theta$