Question

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

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

Short answer

The quadrant in which angle $\theta$lies on 3rd quadrant.

Step-by-step solution

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 $\sin \theta and\mathrm{cs}c\theta arepositveandallothersarenegative$

, in the 3rd quadrant $\tan \theta andcot\theta arepositveandallothersarenegative$

and in the 4th quadrant$\cos \theta andsec\theta arepositveandallothersarenegative$

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

Here $\cos \theta <omeans\cos \theta isnegativeand\tan \theta >o,\tan \theta ispositive,sothesetrignometetricratioslieson3rdquadrant.$

Since$in3rdquadrantonlt\tan \theta >0,cot\theta >oorpositiveandallotherratiosarenegative.$