Question

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

Answer 1

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.