Q. 31 - Precalculus Enhanced with Graphing Utilities

Question

Name the quadrant in which the angle $\theta$ lies.

$\cos \theta >0, \tan \theta <0$

Step-by-Step Solution

Answer

 The quadrant in which angle $\theta$ lies on  fourth quadrant .

Step. 1 Given information

 Here $\cos \theta >0, \tan \theta <0$ is given .

We have to find out  in which angle it lies.

Step 2. Description of the quadrant in which trigonometric functions lies.

  We know that in the first quadrant   all 6 trigonometric functions   $\left(\sin \theta ,\cos \theta ,\tan \theta ,sec\theta ,\mathrm{cs}c\theta ,cot\theta \right)$ are positive. At the second quadrant  only$\sin \theta and \mathrm{cs}c\theta are positve and all others are negative$

In the 3rd quadrant only $\tan \theta and cot\theta are positve and others are negative$

 At the fourth quadrant only $\cos \theta , and sec\theta are positive and all others negative.$

 A figure containing angle lies is given below

Step 3. Description of finding the quadrant in which given angle lies

 we know that  $\cos \theta >0 and sec\theta >0 or postive and all other trignometric functions are negative in forth quadrant.$
  hence  $\cos \theta >0, \tan \theta >0 , in which angle \theta lies on fourth quadrant$