When vectors are oriented away from the ( x ) and ( y ) axes, they can be evaluated using ( x ) and ( y ) components. These components can be linked together in a tip-to-tail fashion which yields the same results as the primary vector in question:
It is useful to imagine the vector above as having opposite ( opp ) and adjacent ( adj ) sides that are accompanied by a right triangle:
We may now place the opposite side of the triangle at the y-axis. This does not alter the expression in any way whatsoever:
Recall that the trigonometric functions established useful relationships between the sides of a right triangle and an angle ( θ ):
sin θ = opp/hyp
cos θ = adj/hyp
tan θ = opp/adj
Furthermore,
hyp sin θ = opp
hyp cos θ = adj
We now have all the information needed to determine the ( x ) and ( y ) components of the vector ( V ):
Vy = V sin θ
Vx = V cos θ
RENAISSANCE PHYSICS 