Page 3a -- Review of Basic Trigonometric Principles

Trigonometry is based on the relationship between cartesian and polar coordinates. A unit circle is defined about an origin such that the orientation of any unit vector in space can be represented in a cartesian system.

This unit vector projected into the first quadrant has been enlarged for simplicity.

The magnitude of the projection on the x-axis is calculated with the COSINE function:

Similarly, the y-axis projection refers to the SINE function:

Combining these equations, we can solve for magnitude and direction of the vector if only the projections are known:

For more details, consult a trigonometry text.