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Chapter 3. Trigonometric Functions

In mathematics, the trigonometric functions (circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component).

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Chapter 2. Relations and Functions

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first components from A and second components from B, and, in particular, a subset of A×A is called a "relation on A." For a binary relation R, one often writes aRb to mean that (a,b) is in R×R.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

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Chapter 1. SETS

A set is a collection of distinct objects, considered as an object in its own right. For example, the numbers1, 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {1,2,4,6}. Sets are one of the most fundamental concepts in mathematics.

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