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Numbers and Their Application - Lesson 16

Trigonometry Continued

Lesson Overview

Trigonometry Introduction

We already covered in lesson 11 the special triangles (3-4-5, isosceles right, and 30°-60°-90°). We also introduced there the basic definitions for right triangle trigonometry:
sin A=opposite/hypotenuse              cos A=adjacent/hypotenuse              tan A=opposite/adjacent
We will have to modify/extend these definitions slightly to generalize them for angles greater than 90° and less than 0° Some authors refer to these generalized definitions as circular functions. We will continue to call either trigonometric functions. The trig functions are part of a general class of functions termed periodic—they repeat. That is, the dependent variable takes on the same set of values over and over again.

Beyond Right Angle Trigonometry

u-v axes. unit circle
Standard position counterclockwise clockwise coterminal Reference angle is the smallest non-negative acute or right angle between the terminal side and either u-axis.
  Sinx   |    All 

 Tanx   |   Cosx 

The Graphs and Periods

Even and Odd functions

Inverse functions, sin-1 x=arcsin x

Principle Values, Sin x vs sin x