Topic: The Six Trigonometric Functions
Subtopic: xyr Definition
Overview
This lesson marks the *real* beginning of trig by introducing the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. While functions like f(x)=x3 have a variable input and an expression output, the trig functions, such as f(θ)=sin(θ), have an angle input and a ratio output. The output is the ratio of two sides of a triangle where the angle, θ pronounced "theta", is an interior angle of the triangle.
We will be defining these functions by expressing the ratio outputs in two different, but equivalent, ways. The first definition we use is the xyr definition meaning that the six trig functions have outputs in terms of the sides of a right triangle, x, y, and r, where r is the hypotenuse.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 1.2.1 Use the xyr definition to find the six trig functions of a given angle
- 1.2.2 Know the sign (positive or negative) of each of the six trig functions in each of the four quadrants
- 1.2.3 Find trig functions of quadrantal angles
Terminology
Memorize the xyr definition of the six trig functions. Memorize and know how to write at least the first 5 letters of the Greek alphabet (see class calendar for link to printable Greek alphabet).