To find an expression equivalent to [tex]\(\cot \theta\)[/tex] given [tex]\(\tan \theta = -\frac{3}{8}\)[/tex], we need to use the relationship between tangent and cotangent. Cotangent is the reciprocal of the tangent, which means:
[tex]\[
\cot \theta = \frac{1}{\tan \theta}
\][/tex]
Let's apply this relationship to the given value of [tex]\(\tan \theta\)[/tex]:
[tex]\[
\tan \theta = -\frac{3}{8}
\][/tex]
So, we will take the reciprocal of [tex]\(\tan \theta\)[/tex]:
[tex]\[
\cot \theta = \frac{1}{-\frac{3}{8}}
\][/tex]
This expression can be simplified by recognizing that taking the reciprocal of a fraction involves flipping the numerator and denominator:
[tex]\[
\cot \theta = -\frac{8}{3}
\][/tex]
Hence, the expression [tex]\(\frac{1}{-\frac{3}{8}}\)[/tex] is equivalent to [tex]\(\cot \theta\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{\frac{1}{-\frac{3}{8}}}
\][/tex]
