**CHAPTER 5, SECTION C:**
*PRELIMINARY DISCUSSIONS ON
HOW TO INTERPRET AND UNDERSTAND THE "NEW-INFORMATION-FROM-OLD"
TYPE IDENTITIES YOU WILL MEET IN THE LATER
SECTIONS OF THIS CHAPTER
*

- assuming a working knowledge of the ideas and geometrical meaning of angles and angular measure, including a familiarity with the use of radians as a unit of angular measure, and
- assuming a familiarity with the Pythagoras' Theorem based
identity sin
^{2}(θ)+cos^{2}(θ)=1, discussed in Section (b) of this chapter. - the idea and geometrical meaning of angles and angular measure (reviewable by reading (or re-reading) Chapter 1 of the course), and
- The basic Pythagoras' Theorem based identity
sin
^{2}(θ) + cos^{2}(θ) = 1 (reviewable by reading (or re-reading) Section (b) of Chapter 5 of the course)

**OVERVIEW:**

This section of Chapter 5 provides a discussion of the intended meanings and uses of identities in which old information of a particular type is used to more easily obtain similar new information. Most of the identities in the remainder of this chapter are of this type. The current section also contains some worked examples to illustrate more explicitly the main point being made. These examples involve identities which will be proved and discussed further in Sections (d), (e) and (f) of this chapter. The examples are worked out BEFORE the results are actually verified in order to help you to understand why these identities might be useful and hence why it is you should be interested in seeing the demonstrations that they are, in fact, true.

This section of the course is basically self-contained, and does not rely in any direct way on any of the other sections of the course, apart from

Links allowing you to review these topics are listed below.

**If you are already familiar with the above background, you can proceed
directly to the contents of the current section of the course by clicking
HERE.
**