[Index]

	Introduction
	Essence
	Memorizing How to memorize Basic Formulas Sum and Difference Formulas Double & Triple Angle Formulas Half Angle Formulas Product to Sum Formulas Sum to Product Formulas All Formulas
	Understanding Page 1 Page 2 Page 3 Page 4 Page 5
	Summarizing Page 1 Page 2
	Examples Examples Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 General ideas
	Exercises
	Final thoughts

4. Understanding the formulas--Page 3

In order to understand formulas very well, we should also know the relationships between some formulas. For example, we get the Sum and Difference formulas from the definitions of trigonometric functions. From Sum formulas, let = = , then we get the Double-Angle formulas. From Double-Angle formulas of cosine:

we get Half-Angle formulas:

In fact the relationship of and is double angle relationship. Sometimes, the following formulas:

(1)

Let , . If we add them together, we have , . From (1), we have: .

(2)

After substituting x and y by and respectively in (2), we have the Sum to Product formula:

From (1) divide by 2 on both sides, we have the Product-to-Sum formula: