Answer:
C) -120/119
Step-by-step explanation:
Use double angle formula:
tan(2θ) = 2 tan θ / (1 − tan²θ)
To find tan θ from sin θ, draw a right triangle in quadrant II. Sine is opposite over hypotenuse, so using Pythagorean theorem, the adjacent side is:
a² + b² = c²
5² + b² = 13²
b = -12
So tan θ = -5/12.
Plugging in:
tan(2θ) = 2 (-5/12) / (1 − (-5/12)²)
tan(2θ) = (-5/6) / (1 − (25/144))
tan(2θ) = (-5/6) / (119/144)
tan(2θ) = (-5/6) × (144/119)
tan(2θ) = -120/119
