Question

If vector A⃗ has components Ax and Ay and makes an angle θ with the +x axis, then...

Answer 1

If vector A⃗ has components Ax and Ay and makes an angle θ with the +x axis, then tanθ = Ay/Ax to get the angle of the vector components. Since the trigonometric function of tanθ is sinθ over cosθ, and since sinθ = y/r and cosθ = x/r.