Question

Find cos θ if sin θ = -12/13 and tan θ > 0.

Answer 1

\[\tan \theta>0,hence \theta lies in first or third quadrant.\]
\[\sin \theta<0,hence \theta lies in third or fourth quadrant.\]
\[from the two \theta lies inthird quadrant.Hence \cos \theta is negative.\]
\[\cos ^{2} \theta +\sin ^{2}\theta=1,\cos \theta=-\sqrt{1-\sin ^{2}\theta} =-\sqrt{1-\left( \frac{- 12 }{ 13 }\right)^{2}}\]
\[=-\sqrt{1-\frac{ 144 }{ 169 }}=-\sqrt{\frac{ 25 }{169 }}=-\frac{ 5 }{13}\]

Answer 2

thank you!