Final answer:
To express the x and y-components of a vector in terms of magnitude and direction, we use the equations: Ax = A cos(theta) and Ay = A sin(theta).
Step-by-step explanation:
To express the x and y-components of a vector in terms of its magnitude, A, and direction, global angle θ, we use the following relationships:
Ax = A cos(θ)
Ay = A sin(θ)
These equations allow us to determine the horizontal and vertical components of a vector based on its magnitude and direction. The x-component (Ax) represents the part of the vector that points in the positive x-axis direction, while the y-component (Ay) represents the part of the vector that points in the positive y-axis direction.
To express the x and y-components of a vector in terms of its magnitude, A, and direction, global angle θ, we use trigonometric relationships.
This is derived from the fact that in a right triangle, the length of the side adjacent to angle θ (the x-component) is the hypotenuse multiplied by the cosine of that angle, and the length of the side opposite angle θ (the y-component) is the hypotenuse multiplied by the sine of that angle. These relationships allow us to decompose a vector into its horizontal and vertical components relative to the x-axis.
The correct answer is a), which states the components as: Ax = A cos(θ) and Ay = A sin(θ).