4.1 - 4.4 test\nno calculators allowed\ndetermine whether the given function is positive or negative for…

4.1 - 4.4 test\nno calculators allowed\ndetermine whether the given function is positive or negative for values of t in the specified quadrant.\n1) quadrant iv, csc t\na) negative\nb) positive

4.1 - 4.4 test\nno calculators allowed\ndetermine whether the given function is positive or negative for values of t in the specified quadrant.\n1) quadrant iv, csc t\na) negative\nb) positive

Answer

Explanation:

Step1: Recall the reciprocal identity

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

Step2: Determine the sign of (\sin t) in Quadrant IV

In Quadrant IV, the (y -)coordinate (which is related to (\sin t) as (\sin t = y) for a point ((x,y)) on the unit - circle corresponding to angle (t)) is negative. So, (\sin t<0) when (t) is in Quadrant IV.

Step3: Determine the sign of (\csc t)

Since (\csc t=\frac{1}{\sin t}) and (\sin t<0), then (\csc t=\frac{1}{\text{negative number}}<0).

Answer:

A. Negative