If \( \sin \theta = -\frac{3}{5} \) and \( \theta \) lies in the third quadrant, find \( \cos \theta \)

Where sin θ = opphyp → 
$\frac{-3}{5}$

opp = -3, hyp = 5

using pythagoras formula 

hyp2 ${}^2$ = adj2 ${}^2$ + opp2 ${}^2$

adj2 ${}^2$ = hyp2 ${}^2$ - opp2 ${}^2$

adj2 ${}^2$ = 52 ${}^2$ - 32 ${}^2$ → 25 - 9

adj2 ${}^2$ = 16

adj = 4

cos θ = adjhyp → 
$\frac{4}{5}$

In third quadrant: cos θ is negative → - 45