Answer:
The value of cosine is \(\frac{12}{13}\).
Step-by-step explanation:
It is given that an angle \({\theta}\), 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
\((Hyp)^2=(Base)^2+(Per)^2\)
⇒\((H)^2=(12)^2+(-5)^2\)
⇒\((H)^2=144+25\)
⇒\((H)^2=169\)
⇒\(H=13\)
Thus, the value of hypotenuse is 13units.
Now, the value of cosine is given as:
\(cosine=\frac{adjacent}{hypotenuse}\)
⇒\(cosine=\frac{12}{13}\)
Therefore, the value of cosine is \(\frac{12}{13}\).
