ANSWER
[tex]\cos( \theta) = - \frac{5\sqrt{61}}{ 61 } [/tex]
EXPLANATION
The given point is (-5,-6).
This implies that ,
[tex] \tan( \theta) = \frac{6}{5} [/tex]
Hence opposite=6 units and adjacent=5 units.
The hypotenuse is,
[tex] = \sqrt{ {5}^{2} + {6}^{2} } = \sqrt{61} [/tex]
Since the terminal side is in the third quadrant, the cosine ratio is negative.
[tex] \cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = - \frac{5}{ \sqrt{61} } [/tex]
Rationalize the denominator,
[tex]\cos( \theta) = - \frac{5\sqrt{61}}{ 61 } [/tex]
The correct choice is C.
