Since sin α = -4/5 and α is in the third quadrant (3π/2 < α < 2π), we can determine that cos α is positive in this quadrant.
We can use the Pythagorean identity cos^2 α + sin^2 α = 1 to find cos α:
cos^2 α + (-4/5)^2 = 1cos^2 α + 16/25 = 1cos^2 α = 1 - 16/25cos^2 α = 9/25
Taking the square root of both sides to find cos α:
cos α = √(9/25)cos α = 3/5
Therefore, cos α = 3/5.
Since sin α = -4/5 and α is in the third quadrant (3π/2 < α < 2π), we can determine that cos α is positive in this quadrant.
We can use the Pythagorean identity cos^2 α + sin^2 α = 1 to find cos α:
cos^2 α + (-4/5)^2 = 1
cos^2 α + 16/25 = 1
cos^2 α = 1 - 16/25
cos^2 α = 9/25
Taking the square root of both sides to find cos α:
cos α = √(9/25)
cos α = 3/5
Therefore, cos α = 3/5.