Question

4.1 - 4.4 test
no calculators allowed
determine whether the given function is positive or negative for values of t in the specified quadrant.

1. quadrant iv, csc t

a) negative
b) positive

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