Question

Please help me. This for an online class.

Answer 1

Look at the picture.

Definitions:

$\sin\theta=\dfrac{y}{r}\\\\\cos\theta=\dfrac{x}{r}\\\\\tan\theta=\dfrac{y}{x}\\\\\cot\theta=\dfrac{x}{y}$

We have the point (-5, -12) → x = -5, y = -12.

Calculate r:

$r=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13$

Substitute to the formula of sin:

$\sin\theta=\dfrac{-12}{13}=-\dfrac{12}{13}$

Answer: a.