Answer
$\tan(-86.9814^\circ)$ is the answer to this exercise.
Work Step by Step
$$\cot176.9814^\circ$$
As cotangent and tangent are cofunctions, $\tan\theta$ is the cofunction needed to find as long as $\theta$ satisfies
$$\tan\theta=\cot176.9814^\circ\hspace{1cm}(1)$$
According to Cofunction Identity: $\tan\theta=\cot(90^\circ-\theta)$
Apply this to the equation $(1)$:
$$\cot(90^\circ-\theta)=\cot176.9814^\circ$$
$$90^\circ-\theta=176.9814^\circ$$
$$\theta=90^\circ-176.9814^\circ=-86.9814^\circ$$
Hence, $\tan(-86.9814^\circ)$ is the answer to this exercise.
