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

Aug 11, 2016

$2$nd Quadrant

Aug 11, 2016

${Q}_{I I}$.

Explanation:

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

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

Let $E = \left\{A \in U : \sin A > 0\right\} , \mathmr{and} , F = \left\{A \in U : \tan A < 0\right\}$

Let ${Q}_{i} , i = I , I I , I I I , \mathmr{and} I V$denote ${i}^{t h}$ Quadrant.

$\Rightarrow E = {Q}_{I} \cup {Q}_{I I} , \mathmr{and} , F = {Q}_{I I} \cup {Q}_{I V}$

Then, the Reqd. Quadrant $= E \cap F$

$= \left({Q}_{I} \cup {Q}_{I I}\right) \cap \left({Q}_{I I} \cup {Q}_{I V}\right)$

$= {Q}_{I I} \cup \left({Q}_{I} \cap {Q}_{I V}\right)$

$= {Q}_{I I} \cup \phi$

$= {Q}_{I I}$, as derived by, Deepak G. !

Enjoy Maths.!