of the angle between two non-zero vectors is given by using the dot product. Comparison of this expression to the definition of the absolute value of the polar sine as given above gives: In particular, for , this is equivalent to which is the Pythagorean theorem. History Polar sines were investigated by Euler in the 18th century. See also Trigonometric functions List of trigonometric identities Solid angle Simplex Law of sines Cross product and Seven-dimensional cross product Graded algebra Exterior derivative Differential geometry Volume integral Measure (mathematics) Product integral References External links Polytopes Trigonometry