Answer:
The value of cosine is [tex]\frac{12}{13}[/tex].
Step-by-step explanation:
It is given that an angle [tex]{\theta}[/tex], with the point (12,-5) is on its terminating side, then the adjacent sides has measure =12 and the opposite side has measure =-5.
Now, from the figure drawn, using the Pythagoras theorem, we have
[tex](Hyp)^2=(Base)^2+(Per)^2[/tex]
⇒[tex](H)^2=(12)^2+(-5)^2[/tex]
⇒[tex](H)^2=144+25[/tex]
⇒[tex](H)^2=169[/tex]
⇒[tex]H=13[/tex]
Thus, the value of hypotenuse is 13units.
Now, the value of cosine is given as:
[tex]cosine=\frac{adjacent}{hypotenuse}[/tex]
⇒[tex]cosine=\frac{12}{13}[/tex]
Therefore, the value of cosine is [tex]\frac{12}{13}[/tex].
