Algebra-2

In standard position, the initial side of the angle is the positive x-axis, and the terminal side is the line segment that forms the angle with the positive x-axis. Since the terminal side passes through the point , it is a vertical line segment that extends 4 units above the origin.

Now, let's consider the right triangle formed by the terminal side, the x-axis, and the vertical line segment from the origin to the terminal side. Since the terminal side is 4 units above the origin, the length of the vertical line segment is 4.

The hypotenuse of the right triangle is the distance from the origin to the point , which is simply the length of the vertical line segment, i.e., 4.

Using the definition of cosine in a right triangle, we have:

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