Module 5-I – Introduction to Trigonometry 

Introduction

 The next main class of functions for us to consider are those that arise from the study of trigonometry. These have many uses, especially for modelling all kinds of cyclical phenomena. But before going ahead with the study of these important functions, we’ll first take a break from our study of functions in order to review the basics of trigonometry itself and its uses in geometric applications.

 The word 'Trigonometry' translates (from Greek) literally as 'measurement of triangles', but although triangles occur throughout the subject, it is also the basic tool for understanding relationships between lengths and angles in any context, and so is an invaluable tool in many geometric and physical problems.

Learning Objectives

 In this Module you will review some basic geometry and the definitions and uses of  trigonometry.  After completing this Module you will be able to:

·  Recognize applied situations involving basic geometry

·  Work with various units for the measurement of angles

·  State the definitions of the six trigonometric ratios

·  Use trigonometric methods to solve geometric problems involving right angled triangles

·  State the ‘Law of Sines’ and ‘Law of Cosines’ and use these to solve geometric problems involving non-right-angled triangles

Module Outline and Section Learning Objectives

Section 1 – Geometric Review

·              Identify similar triangles in a geometric diagram, and use the similarity to compute unknown lengths in terms of known ones

·              Identify right angled triangles in a geometric diagram, and use the pythagoras’ theorem to compute unknown lengths in terms of known ones

·              Identify the basic geometry involved in various applied situations and solve problems arising from such situations

Section 2 – Measurement of Angles

·              Define the degree, minute, second and radian units of angular measurement

·              Convert  the description of an angle from one unit to another

·              Quickly estimate the measure of a given angle in any of these units

·              Solve geometric and applied problems involving the determination of arc lengths in terms of angles

 Section 3 – Trigonometric Ratios

·              State the definitions of the six trig ratios

·              Find the values of all six trig ratios for an any angle in a right angled triangle whose side lengths are specified (or even if just two are)

·              Recognize special cases of angles whose trig ratios can be determined exactly in terms of radicals by using basic geometry

·              Use a calculator or tables to determine approximate trig ratios for any given angle

·              Determine all of the sides of a right triangle given one side and one of the acute angles

·              Recognize and solve applied problems using these skills

 Section 4 – Applications Involving Right Triangles

·              Use measurement of angles to calculate the dimensions of large or distant objects

·              Use compass bearings and known distances to determine other distances and locations

·              Recognize and solve applied problems using these skills

 Section 5 – Law of Sines and Law of Cosines

·              State the Law of Sines and the Law of Cosines

·              Use these laws to help solve geometric problems involving general triangles

Go To: Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Lab