Respuesta :
Answer:
[tex]cos\theta=\frac{-2}{\sqrt{85} }[/tex]
Step-by-step explanation:
Let's call r the distance form the origin to the point (-2,9), this distance is related with [tex]cos\theta[/tex] with the expression
[tex]x=rcos\theta\\cos\theta=\frac{x}{r}[/tex]
So, we have to find r with the formula of distance and the given point:
[tex]r=\sqrt{x^{2}+y^{2}}=\sqrt{(-2)^{2}+(9)^{2} }\\r=\sqrt{4+81}=\sqrt{85}[/tex]
Now, replacing on the first relation, we have
[tex]cos\theta=\frac{-2}{\sqrt{85} }[/tex]
Therefore, the answer is
[tex]cos\theta=\frac{-2}{\sqrt{85} }[/tex]
PD: choices were written wrong.
