Question

the terminal side of theta passes through the point (-5,-6). what is the exact value of cos theta in simplified form?

Answer 1

ANSWER

$\cos( \theta) = - \frac{5\sqrt{61}}{ 61 }$

EXPLANATION

The given point is (-5,-6).

This implies that ,

$\tan( \theta) = \frac{6}{5}$

Hence opposite=6 units and adjacent=5 units.

The hypotenuse is,

$= \sqrt{ {5}^{2} + {6}^{2} } = \sqrt{61}$

Since the terminal side is in the third quadrant, the cosine ratio is negative.

$\cos( \theta) = - \frac{adjacent}{hypotenuse}$

$\cos( \theta) = - \frac{5}{ \sqrt{61} }$

Rationalize the denominator,

$\cos( \theta) = - \frac{5\sqrt{61}}{ 61 }$

The correct choice is C.