Question

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

Answer 1

Well, in order to answer this problem we need to use the the Pythagorean Theorem and the  it will be like this:
cos = x / hypotenuse
cos= 12/13 
I think with this you can figure the rest out. Hope this helps

Answer 2

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 $\frac{12}{13}$.