Question

2 multiple choice 1 point determine whether the given function is positive or negative for values of t in the specified quadrant. quadrant ii; cot t negative positive

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