Math Review of Real, Complex, and Hyperreal Numbers

Overview Real numbers are the rational and irrational numbers that people deal with in everyday life. Hyperreal numbers include numbers that are infinitely large, infinitely small, or infinitesimal, along with the reals. Surreal numbers include the reals, the hyperreals, and other constructs in advanced mathematics that sometimes behave like numbers and sometimes do not. Rational […]

Math Review of Platonic Solids and Polyhedra

Overview There are infinitely many regular polygons. However, there are a fixed number of regular polyhedra, called Platonic solids. Mathematicians use the definitions of the regular polygons and the characteristics of solid objects to arrive at their conclusions. Characteristics of Regular Polyhedra Regular polygons, such as equilateral triangles, squares, equilateral pentagons, hexagons, heptagons, octagons, and […]

Math Review of Applications of Circular Functions

Overview Circular trigonometric functions can be applied to situations in physical, biological, and social sciences involving data that follows a pattern that is not linear. Many of those patterns are periodic, and can be modeled by approximations of sine, cosine, or other functions. The Sine and Cosine Waves The numerical value of t around the […]

Math Review of Angles and Circular Motion

Overview Trigonometry is defined by the measurement of angles and their relationships. One of the ways that trigonometry can be applied is in the measurement of angles and circular motion. Angle Measure Angles in trigonometry and calculus can be measured in radians, which is a relationship of the measurement of an angle by the arc […]

Math Review of Trigonometric Identities

Overview Trigonometric identities are relationships between trigonometric ratios that define them in terms of one another. They can be used to help solve problems that involve trigonometric functions. Reciprocal Identities The reciprocal function to the sine is the cosecant, to the cosine is the secant, and to the tangent is the cotangent. In math language, […]