本文第一章主要介紹三角學裡三角函數的定義及基本性質，如和角公式、差角公式、積化和差及和差化積。這些式子提供有效的方法來解決三角學裡的問題。
第二章則是敘述三角學裡兩個最重要的定理：正弦定理與餘弦定理。並且介紹由這兩個定理可推得其他重要的定理，如托勒密定理、尤拉三角公式、西瓦定理、孟氏定理、平行四邊形定理、史都華定理、Brahmagupta’s 公式。另外會討論一些計算三角形面積的定理，如海龍公式、皮克定理。
第三章會說明其它三角學裡重要的概念：正餘弦函數疊合、反三角函數、複數的極式及棣美弗定理。

Chapter 1 presents the definitions and basic properties of trigonometric functions including: Sum Identities, Difference Identities, Product-Sum Identities and Sum-Product Identities. These formulas provide effective tools to solve the problems in trigonometry.
Chapter 2 handles the most important two theorems in trigonometry: The laws of sines and cosines and show how they can be applied to derive many well known theorems including: Ptolemy’s theorem, Euler Triangle Formula, Ceva’s theorem, Menelaus’s Theorem, Parallelogram Law, Stewart’s theorem and Brahmagupta’s Formula. Moreover, the formulas of computing a triangle area like Heron’s formula and Pick’s theorem are also discussed.
Chapter 3 deals with the method of superposition, inverse trigonometric functions, polar forms and De Moivre’s Theorem.

表目錄iii
圖目錄iv
中文摘要vi
Abstract vii
第一章三角函數的基本關係1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 度與弧度. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 三角函數的定義. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 三角函數的關係. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 三角函數的圖形. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 和差角公式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.7 和差角公式應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.8 習題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.8.1 三角函數的定義. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.8.2 三角函數的關係. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.8.3 三角函數的圖形. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.8.4 和差角公式應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.8.5 綜合應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
第二章正弦與餘弦定理的應用35
2.1 正弦與餘弦定理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2 正弦定理之應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 餘弦定理之應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4 習題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4.1 正弦與餘弦定理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.4.2 正弦定理之應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.4.3 餘弦定理之應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.4.4 綜合應用. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


第三章三角學的重要概念78
3.1 正餘弦函數的疊合. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2 反三角函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3 複數的極式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4 習題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4.1 反三角函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4.2 複數的極式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A 簡稱、符號對照表88
A.1 簡稱. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.2 符號. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
B 三角學重要的定義及公式89
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