11. If cos θ = –3/5 and θ lies in Quadrant III, find the exact values of sin θ.

Answer 1

It forms a 3-4-5 right triangle, or -3 - -4 - 5 right triangle.

sin(theta) = -4/5 =-0.8

in 3rd quadrant, cosines & sines are all negative 3^2+4^2 = 5^2, 9+16=25

Answer 2

Using the Pythagorean Theorem, (-3)² + y² = 5² or y = 4 but, we can see that this is a negative (going down in Q3) so y = -4

sin(θ) = opposite/hypotenuse = -4/5