Notice when we drew the velocity vector for our Smart Car, we also put in two smaller arrows. These arrows point exclusively in the x and y directions, and are the x and y components of the velocity vector. These components make a triangle with the velocity vector, which is the hypotenuse.
The mathematical study of triangles is called trigonometry, and one thing trigonometry is useful for is working with vectors. Even if you don’t know trigonometry, you’ve probably messed with the SIN, COS, and TAN buttons on a calculator. We can use the definition of a cosine (COS) to find the length of the x-component. On a calculator, type in 30, hit COS, and multiply that number by the hypotenuse (45 mph). You find that in the x direction only, the car is moving 39 mph.

Notice when we drew the velocity vector for our Smart Car, we also put in two smaller arrows. These arrows point exclusively in the x and y directions, and are the x and y components of the velocity vector. These components make a triangle with the velocity vector, which is the hypotenuse.

The mathematical study of triangles is called trigonometry, and one thing trigonometry is useful for is working with vectors. Even if you don’t know trigonometry, you’ve probably messed with the SIN, COS, and TAN buttons on a calculator. We can use the definition of a cosine (COS) to find the length of the x-component. On a calculator, type in 30, hit COS, and multiply that number by the hypotenuse (45 mph). You find that in the x direction only, the car is moving 39 mph.