Q. 32 - 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 3rd 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 lie.

A figure containing angle lies is given below 

Based on the figure we can easily understand that in the first quadrant all trigonometric ratios are positive, in the 2nd-second quadrant $\sin \theta and \mathrm{cs}c\theta are positve and all others are negative$

 , in the 3rd quadrant $\tan \theta and cot\theta are positve and all others are negative$

and in the 4th quadrant $\cos \theta and sec\theta are positve and all others are negative$

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

Here $\cos \theta <o means \cos \theta is negative and \tan \theta >o ,\tan \theta is positive , so these trignometetric ratios lies on 3rd quadrant.$

Since $in 3rd quadrant onlt \tan \theta >0, cot\theta >o or positive and all other ratios are negative.$