If sin A > 0 and tan A < 0, then A is in what quadrant?

Question

5959 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-11T17:36:11

Aug 11, 2016

$2$ nd Quadrant

Answer 2 · 2016-08-11T18:02:12

$Q_(II)$ .

As we want to determine the Quadrant of $A$ , in what follows our

Universal Set $U$ will be $[0,2pi]$ .

Let $E={A in U : sinA>0}, and, F={A in U : tanA<0}$

Let $Q_i, i=I,II, III, and IV$ denote $i^(th)$ Quadrant.

$rArr E=Q_IuuQ_(II), and, F=Q_(II)uuQ_(IV)$

Then, the Reqd. Quadrant $=EnnF$

$=(Q_IuuQ_(II))nn(Q_(II)uuQ_(IV))$

$=Q_(II)uu(Q_InnQ_(IV))$

$=Q_(II)uuphi$

$=Q_(II)$ , as derived by, Deepak G. !

Enjoy Maths.!