Question

If Sin A = 3/5, and Cos A < 0, find Tan A

Answer 1

\[\sin A=\frac{ 3 }{ 5 }>0,\]
Hence A lies in 1st and 2nd quadrant.
\[\cos A<0,\]
hence A lies in 2nd and 3rd quadrant,
combining we get
A lies in 2nd quadrant
\[\cos A=-\sqrt{1-\sin ^2 A}=-\sqrt{1-\left( \frac{ 3 }{ 5 } \right)^2}=-\frac{ 4 }{ 5}\]
\[\tan A=\frac{ \sin A }{ \cos A }=\frac{ \frac{ 3 }{ 5 } }{ -\frac{ 4 }{ 5 } }=-\frac{ 3 }{ 4 }\]