2 multiple choice 1 point determine whether the given function is positive or negative for values of t in…

Explanation:

Step1: Recall the sign of trigonometric functions in quadrants

In Quadrant II, (x<0) and (y > 0). The cotangent function is defined as (\cot t=\frac{\cos t}{\sin t}).

Step2: Determine the sign of (\cos t) and (\sin t) in Quadrant II

In Quadrant II, (\sin t>0) (since (y>0)) and (\cos t < 0) (since (x < 0)).

Step3: Find the sign of (\cot t)

Since (\cot t=\frac{\cos t}{\sin t}), and (\cos t<0), (\sin t>0), then (\cot t=\frac{\text{negative}}{\text{positive}}<0).

Answer:

Negative