When working with vectors, it is often necessary to resolve a vector into its component parts. To introduce this technique, we are going to use as our reference frame the rectangular grid of the x|y plane common to students from their work in Algebra I and Algebra II.

 

When we speak of a "diagonal force vector" we mean a vector which points towards the interior of a quadrant, not one that lies along the x- or y-axis.

 

Much of what we are going to discuss goes back to former lessons on properties of vectors and basic trigonometry.

 

 

Note that no matter into which "quadrant" your vector points, angle ϴ should always next to the x-axis, it is called the reference angle.

 

As you will see in some of the following examples, if the given angle is not in standard position then you can always use geometry to find the angle next to the nearest x-axis.  Alternatively, the component called "cosine" is always adjacent to whichever angle is given and the second component is always called "sine."