Point P (8, -4) is on the terminal arm of angle theta

What quadrant would this be in? Cosine?

cosine is not a quadrant.

With x positive and y negative, that is QIV
cosine = x/r

To determine the quadrant of a point on the coordinate plane, we need to examine the signs of its x and y coordinates. In this case, the point P(8, -4) has a positive x-coordinate and a negative y-coordinate.

Since the x-coordinate is positive and the y-coordinate is negative, we can conclude that the point P lies in the fourth quadrant. The fourth quadrant is located below the x-axis and to the right of the y-axis.

Now, as for the cosine of the angle theta, we need more information to calculate it. The cosine function relates the adjacent side of a right triangle to the hypotenuse. To find the cosine of an angle, we need the lengths of the adjacent side and the hypotenuse. The point P alone does not provide sufficient information to determine those lengths.

If you have additional information, such as the length of the adjacent side or the angle theta, please let me know, and I can assist you further in calculating the cosine.