16 multiple choice 1 point determine the sign (positive or negative) of the given value without use of a…

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:

16. Positive
17. Negative