Algebra is the study of real numbers. Arithmetic deals directly with these numbers, but Algebra tells us how to represent them symbolically and then to manipulate the symbols by specific rules to solve problems that could not be approached simply by looking at the numbers directly.

Trigonometry studies the relationship between the angles and the ratio of the sides of a right triangle with important applications in surveying and physics.
Often Precalculus is taught in such a way that includes only the fundamental and necessary knowledge of the mathematics techniques that are a foundation to Calculus without providing any hint at the beauties found in Calculus. By including topics in sequences and series and limits, then a taste of Calculus can be experienced and enjoyed!