To determine the value of [tex]\(\cot \theta\)[/tex] given that [tex]\(\tan \theta = \frac{11}{60}\)[/tex], we need to use the relationship between the tangent and cotangent functions. Specifically, we use the identity:
[tex]\[
\cot \theta = \frac{1}{\tan \theta}
\][/tex]
Given:
[tex]\[
\tan \theta = \frac{11}{60}
\][/tex]
We can substitute this value into the identity:
[tex]\[
\cot \theta = \frac{1}{\frac{11}{60}}
\][/tex]
Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore:
[tex]\[
\cot \theta = 1 \div \frac{11}{60} = 1 \times \frac{60}{11} = \frac{60}{11}
\][/tex]
Thus, the value of [tex]\(\cot \theta\)[/tex] is [tex]\(\frac{60}{11}\)[/tex].
The correct answer is:
[tex]\[
\frac{60}{11}
\][/tex]
