Module 5-II – Trigonometric Functions

Section 5-II.1 – Definitions and Evaluation

 

Introduction

 

If, for each value of t between 0 and 90, we construct an angle of , build a right triangle, and measure its sine ratio, then the result will define a function of t with . If we use a different method of measuring angles then for a given value of the number t we’ll be looking at a different angle and so get a different result. So we’ll get a different function. For example, the functions , and  are both different from .( If you put in a particular number, like 1/4, for t , they will give different results). Of course, since an angle of t degrees is the same as an angle of  radians, we have  and so the functions are related, but they are not the same.

It turns out that the functions defined using radian measure are more convenient for many purposes (especially in calculus) so these are the ones we’ll focus on, and it is just for these that we use the name of the trigonometric ratio as the name of our function. (So, we’ll use the name  just for the case of  above.) This section is devoted to introducing these functions and studying their basic properties.

 

 

What to Do

 

1.                  Read the Study Notes and Discussion, and make sure that you have absorbed the main points by answering the questions.

 

2.                  Read sections 5.3 and 5.4 of the text

3.         Follow the instructions regarding Further Practice until you have achieved the Learning Objectives for this section.

 

Go To:    Sec 5-II.0    Sec 5-II.1    Sec 5-II.2    Sec 5-II.3    Sec 5-II.4      Lab