Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-$\tan \theta$, given that $\cot \theta = \frac { \sqrt { 5 } } { 4 }$
A) $\frac { \sqrt { 4 } } { 5 }$

B) $\frac { 4 \sqrt { 5 } } { 5 }$

C) $\frac { \sqrt { 5 } } { 5 }$

D) $\frac { 5 \sqrt { 5 } } { 4 }$

Question

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-$\tan \theta$, given that $\cot \theta = \frac { \sqrt { 5 } } { 4 }$
A) $\frac { \sqrt { 4 } } { 5 }$

B) $\frac { 4 \sqrt { 5 } } { 5 }$

C) $\frac { \sqrt { 5 } } { 5 }$

D) $\frac { 5 \sqrt { 5 } } { 4 }$

Quizplus · Accepted Answer

The identity relating $\tan \theta$ and $\cot \theta$ is $\tan \theta = \frac{1}{\cot \theta}$. Given $\cot \theta = \frac{\sqrt{5}}{4}$, $\tan \theta = \frac{1}{\frac{\sqrt{5}}{4}} = \frac{4}{\sqrt{5}}$. Rationalizing the denominator gives $\tan \theta = \frac{4\sqrt{5}}{5}$.

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

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