Angle θ is in standard position. If tanθ < 0 and cosθ = - 4/5, find sinθ.

Use the formula,

sin^2 x + cos^2 x = 1

sin^2 x + (-4/5) ^2 = 1

sin^2 x + 16/25 = 1

sin^2 x = 1-16/25

sin^2 x = (25-16) / 25

sin^2 x = 9/25

sin x = + 3/5 or - 3/5

since both tan and cos are negative, sine will be positive (Quadrant 2).

sin x = 3/5.