The terminal ray of an angle passes through the point (5,12).

What is the value of cosine for this angle?

x = 5

y = 12
therefore,
r = √(12² + 5²) = 13

recall that cosθ = x/r
therefore...

cosθ = 5/13

To find the value of cosine for this angle, we need to know the coordinates of the initial and terminal rays of the angle. The coordinates of the terminal ray are given as (5,12).

However, to calculate the cosine of an angle, we need to know one of the other two sides of a right triangle formed by the angle. Since we only have the coordinates of a single point, we don't have enough information to directly determine the length of any side of the triangle.

To find the value of cosine for this angle, we need additional information such as the length of one of the other two sides of the triangle or the angle measure itself.

To determine the value of cosine for the angle whose terminal ray passes through the point (5,12), we need to find the cosine of the angle with respect to the x-axis.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, we can consider the x-coordinate of the given point (5,12) as the adjacent side and the distance from the origin to the point as the hypotenuse.

To find the distance from the origin to the point (5,12), we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the point and the origin (0,0):

distance = √((5 - 0)^2 + (12 - 0)^2)
distance = √(25 + 144)
distance = √169
distance = 13

So, the distance from the origin to the point (5,12) is 13.

Now, we can find the cosine of the angle:

cosine of the angle = adjacent side / hypotenuse
cosine of the angle = 5/13

Therefore, the value of cosine for the angle whose terminal ray passes through the point (5,12) is 5/13.