Chapter 12.3, Problem 28OE

To determine

Name the quadrant of $\theta$ .

Answer to Problem 28OE

Quadrant III

Explanation of Solution

Given:

  $\tan \theta >0,90°<\theta <270°$

Formula Used:

Function value	Quadrant of $\theta$ Is I	Quadrant of $\theta$ Is II	Quadrant of $\theta$ Is III	Quadrant of $\theta$ Is IV
$\begin{array}{l}\sin \theta \\ \csc \theta \end{array}$	+	+	-	-
$\begin{array}{l}\cos \theta \\ \sec \theta \end{array}$	+	-	-	+
$\begin{array}{l}\tan \theta \\ \cot \theta \end{array}$	+	-	+	-

Calculation:

  $90°<\theta <270°$ , implies Quadrant II and III ; from the table , the condition of $\tan \theta >0$ is satisfied in Quadrant III.