Look at the picture.
Definitions:
[tex]\sin\theta=\dfrac{y}{r}\\\\\cos\theta=\dfrac{x}{r}\\\\\tan\theta=\dfrac{y}{x}\\\\\cot\theta=\dfrac{x}{y}[/tex]
We have the point (-5, -12) → x = -5, y = -12.
Calculate r:
[tex]r=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13[/tex]
Substitute to the formula of sin:
[tex]\sin\theta=\dfrac{-12}{13}=-\dfrac{12}{13}[/tex]
Answer: a.
