We are asked to find cos θ if:
sin θ = -3/5 and it is in the third quadrant.
first lets find the adjacent:
Let the triangle be ABC.
Since sin θ = -3/5
AB/AC = 3/5
Let AB = 3x
then AC = 5x
In a right angled triangle ABC,
By pythagoras theorem,
We get
(5x)² = (3x)² + BC²
BC² = (5x)² - (3x)²
BC² = (2x)²
BC = 4x
Recall Cos θ = Adjacent/Hupotenuse
= BC/AC
= 4x/5x
= 4/5
Since its in the third quadrant and cos is negative in the third quadrant, therefore,
Cos θ = -4/5
So, the correct option is A, which is -4/5.