Answer
$-\dfrac{5\sqrt{146}}{146}$
Work Step by Step
First determine $x,y$ and $r$:
$(x,y)=(-5,11)$
$x=-5$
$y=11$
Solve for $r$ using the formula $r^2=x^2+y^2$:
$r^2=x^2+y^2\\
r^2=(-5)^2+11^2\\
r^2=146\\
r=\pm\sqrt{146}$
Since $r$ is never negative, then $r=\sqrt{146}$.
Compute $\cos\theta$:
$\cos\theta=\dfrac{x}{r}=\dfrac{-5}{\sqrt{146}}=\dfrac{-5\cdot \sqrt{146}}{\sqrt{146} \cdot \sqrt{46}}=-\dfrac{5\sqrt{146}}{146}$
