Question

If sin Θ = 2 over 3 and tan Θ < 0, what is the value of cos Θ?

Answer 1

\[\sin \theta=\frac{ 2 }{ 3 },\tan \theta <0\]
hence theta lies in second quadrant ,where cos theta is negative.

Answer 2

\[\cos \theta=-\sqrt{1-\sin ^2\theta }\]

Answer 3

I'm confused

Answer 4

\[\cos ^2 \theta +\sin ^2 \theta=1\]
\[\cos ^ 2 \theta =1-\sin ^2 \theta \]
\[\cos \theta =\pm \sqrt{1-\sin ^2 \theta }\]
as \[\sin \theta =\frac{ 2 }{ 3 }>0,\tan \theta <0 \]
\[\sin \theta >0 shows ~that~\theta~lies~\in~1st~or~2nd ~quadrant.\]
\[\tan \theta <0,\theta \in ~2nd~or~4th~quadrant.\]
combining theta lies in 2nd quadrant.
\[\cos \theta=-\sqrt{1-\sin ^2 \theta }=-\sqrt{1-\left( \frac{ 2 }{ 3 } \right)^2}=?\]