Question

16 multiple choice 1 point determine the sign (positive or negative) of the given value without use of a calculator. sin 141° positive negative 17 multiple choice 1 point determine whether the given function is positive or negative for values of t in the specified quadrant. quadrant iv, csc t positive negative

Explanation:

Step1: Determine the quadrant of \(141^{\circ}\)

Since \(90^{\circ}<141^{\circ}<180^{\circ}\), \(141^{\circ}\) is in the second quadrant.

Step2: Recall the sign of sine in different quadrants

In the second quadrant, \(\sin\theta> 0\). So, \(\sin141^{\circ}>0\).

Step3: Recall the relationship between \(\csc t\) and \(\sin t\)

We know that \(\csc t=\frac{1}{\sin t}\).

Step4: Determine the sign of \(\sin t\) in Quadrant IV

In Quadrant IV, \(\sin t < 0\).

Step5: Determine the sign of \(\csc t\)

Since \(\csc t=\frac{1}{\sin t}\) and \(\sin t<0\) in Quadrant IV, then \(\csc t<0\).

Answer:

1. Positive
2. Negative