Lesson Plan

Define the x- and y-components of a two-dimensional vector

Resolve a vector into components using A_x = A cos θ and A_y = A sin θ

Reconstruct a vector's magnitude and direction from its components using A = √(A_x² + A_y²) and θ = tan⁻¹(A_y/A_x)

Add and subtract vectors analytically using the four-step component procedure

Apply the quadrant rule to interpret the inverse-tangent result correctly

5.2

"For a two-dimensional vector, a component is a piece of a vector that points in either the x- or y-direction. Every 2-d vector can be expressed as a sum of its x and y components." "To find the magnitude A and direction θ of a vector from its perpendicular components A_x and A_y, we use the following relationships: A = √(A_x² + A_y²), θ = tan⁻¹(A_y/A_x)." "Note that tan⁻¹(θ) gives an angle in the first quadrant if A_y/A_x > 0 and in the fourth quadrant if A_y/A_x < 0. If, in fact, both A_x and A_y are negative, or if A_x is negative and A_y positive, then θ, measured from the positive x direction, is tan⁻¹(θ) + 180°."