We saw how you can use trigonometry to find the components of a vector. If a car’s velocity vector is 45 mph at a 30 degree angle to the x-axis, you can use the cosine of 30 to figure out it’s moving 39 mph in the x-direction. Using the sine of 30 you can find it’s going 22.5 mph in the y-direction.
A way to write this mathematically is with i and j notation. The letters i and j are unit vectors in the x and y direction respectively. The x component is multiplied times i and the y component is multiplied times j. Our vector for a car moving at 45 mph at a 30 degree angle is formally written as v = 39i + 22.5j and you can include the mph (units) if you want to be super correct.