Question

For an angle θ with the point (−5, −12) on its terminating side, what is the value of cosine?

Options:
A. -5
B. -12
C. -5/13
D. -12/13

Answer 1

option C.
`-(5)/(13)`

Explanation:

we have that

The point (-5,-12) belong to the III quadrant

so

The value of the cosine is negative

Applying the Pythagoras Theorem

Find the value of the hypotenuse

`h^(2)=5^(2)+12^(2)\\ h^(2) =25+144\\ h^(2)=169\\h=13\ units`

The value of cosine of angle θ is the ratio between the side adjacent to angle θ and the hypotenuse

`cos(\theta)=-(5)/(13)`