Which trigonometric function, when multiplied by a vector's magnitude, gives the x-component of a vector oriented at an angle with respect to the x-axis in a coordinate system?

In a coordinate system, when a vector is oriented at an angle θ with respect to the x-axis, its x-component can be found using the cosine function. The x-component (V_x) is equal to the vector's magnitude (V) multiplied by the cosine of the angle (θ):
 

Vx​=V cosθ

 


This relationship comes from the definition of the cosine function in a right triangle, where the adjacent side (x-component) is equal to the hypotenuse (vector's magnitude) multiplied by the cosine of the angle. This is a fundamental concept in vector decomposition.