Direction Cosines and Coordinate Direction Angles [Introduction]

In this video, we introduce the idea of direciton cosines and coordinate direction angles. We use direction cosines as a way to express the components of a vector or unit vector. Though difficult to visualize for vectors in 3D space, coordinate direction angles and direction cosines have nice properties. Coordinate direction angles are always less than 180 degrees and direction cosines will automatically take care of negative components (when the coordinate direction angle is above 90 degrees). We can also use direction cosines as a quick way to find a unit vector using vector components. Using the fact that unit vectors have a magnitude of 1, knowing two coordinate direction angles allows us to solve for the third angle using Pythagorean Theorem.