Algebra and Trigonometry

Algebra allows you to converse using variables. It allows you to set up equations. It allows you to explore the properties of numbers. It also allows you to explore how to graph equations using the Cartesian coordinate system. When you can graph the relations you explore using algebra, you find that you begin examining the behavior of numbers as specific types of patterns.

Math might be viewed as a way of formally expressing patterns. Likewise, everything can be viewed as a pattern. Some patterns are found. Others are created. The serrations of a leaf or the path of a ball when you toss it are patterns that you find. On the other hand, at times you fidget with math and find a pattern, and then go looking for something in nature you can use to illustrate the pattern.

Algebra in part deals with patterns you can explore using linear and nonlinear relations between sets of numbers. You find one set of numbers, for example, and then map this set of numbers to another set. The map is an equation.

Trigonometry extends the ways that you can map one set of numbers to another. It begins with explorations of triangles. A triangle allows you to bring three values into different relations with each other. These relations constitute the trigonometric ratios.

The ratios of trigonometry allow you to extend the notion of patterns to encompass the different ways that patterns can behave. Among other things, patterns can be periodic. One period pattern is known as the sine wave. Another is known as a cosine wave. From cosines and sines you can continue on to tangents, cotangents, secants, and cosecants.

Algebra and trigonometry together provide a foundation for the study of calculus. They allow you to explore relationships between sets of numbers and to generate graphical representations of these relationships in a multitude of ways.

They are usually viewed as fundamental mathematics, although there are disciplines of mathematics in which trigonometry and algebra are studied on advanced levels. As it is, in the context provided here, the objective remains one of inviting you to explore math in a conversational way. Everyone can learn something. Each act of learning is an act of confirmation. Each act of learning becomes a way to make what is strange familiar. Each act of learning is a way to extend what you know into new places.