In a coordinate system, a vector is oriented at angle theta with respect to the x-axis. the x component of the vector equals the vector's magnitude multiplied by which trigonometric function?

Cosine. The cosine is a ratio of the adjacent side of a right triangle to the hypotenuse. In this case, the horizontal component is the adjacent side and the vector is the hypotenuse. When multiplying the magnitude of the vector by cosine of theta, the magnitudes will cancel, leaving the horizontal component as your answer.