math

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and are widely used for studying periodic phenomena through Fourier analysis.

A vector has magnitude (how long it is) and direction ... Here are two vectors

A introduction to representing vectors using the standard Cartesian coordinate systems in the plane and in three-dimensional space.

In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.

In this video I go over a method for determining if 3 points lie on the same line by using the cross product of any 2 position vectors formed from the points. If the cross product is zero then the points all lie on the same line.

In this video I review how to determine whether two vectors or planes are parallel or perpendicular. Two vectors are parallel of their cross product is zero, and are perpendicular if their dot product is zero. The angle between two planes can be determining the angle between their normal vectors: if the angle is zero then the planes are parallel.

In this video I show that we can determine the angle between two intersecting planes by computing the dot product of their normal or perpendicular vectors.

In this video I show that the cross product of two non-parallel vectors on a plane obtains a vector perpendicular to that plane, and is called the normal vector.

calculus - Geometric intuition for derivatives of basic trig functions - Mathematics Stack Exchange

Linear quadratic gaussian LQG with servo controller