Sin α = -4/5,3п/2<а<2п. найти cos a

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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.