Answer:
-15/17
Step-by-step explanation:
One method is to use Pythagorean identity.
sin² θ + cos² θ = 1
sin² θ + (-8/17)² = 1
sin² θ + 64/289 = 1
sin² θ = 225/289
sin θ = ±15/17
Since θ is in the third quadrant, sin θ < 0. So sin θ= -15/17.
Another method is to draw a triangle in the third quadrant, with angle θ, adjacent side -8, and hypotenuse 17. Use Pythagorean theorem to find the opposite side:
c² = a² + b²
17² = (-8)² + b²
b = -15
Therefore, sin θ = -15/17
