Use a sum or difference identity to find the exact value.
-Find $\cot \theta$ if $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.
A) $\frac { 3 \sqrt { 7 } } { 7 }$
B) $- \frac { 3 } { 2 }$
C) $\frac { 5 } { 4 }$
D) $- \frac { \sqrt { 7 } } { 9 }$

Question

Quizplus · Accepted Answer

The cotangent is the reciprocal of the tangent. Given $\tan \theta = \frac{\sqrt{7}}{3}$, $\cot \theta = \frac{1}{\tan \theta} = \frac{3}{\sqrt{7}}$. To express this in simplest radical form, multiply the numerator and denominator by $\sqrt{7}$ to get $\frac{3\sqrt{7}}{7}$. Since $\theta$ is in the third quadrant, where both sine and cosine (and thus tangent and cotangent) are negative, the positive result indicates a misunderstanding of the quadrant's impact. However, given the options and the direct calculation, option A is the closest to the correct process despite the sign discrepancy.

Use a Sum or Difference Identity to Find the Exact cot⁡θ\cot \thetacotθ

Use a Sum or Difference Identity to Find the Exact $\cot \theta$