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Discovering Mathematics is a series of textbooks designed for the students in secondary schools. It follows the secondary Mathematics syllabus issued by the Ministry of Education, Singapore, which will be implemented from 2007 onwards. This series of Mathematics books covers the entire syllabus for the Singapore-Cambridge GCE O-Level Mathematics.

The emphasis of this series is on empowering students to learn mathematics effectively and independently. Depending on the topic covered, different approaches are adopted for the presentation of concepts to facilitate easy understanding by students. In some topics, an intuitive or an experimental approach is adopted to enable students to internalize concepts and instill in them an interest to explore the topics further.

Some features of this series include the following:

1. Class activities which allow the student to learn mathematics through discovery. Some of the class activities make use of Geometer’s Sketchpad (available at www.keypress.com).
2. Worked examples are followed by a similar question (Try It!) so that students can chek if they have understood the concepts presented earlier.
3. Every lesson has an exercise. The questions in the exercise are sequenced as Basic Practice (simple questions involving a direct application of the concepts, Further Practice (more challenging questions on direct application, Maths@Work (questions that apply mathematical concepts to real-life situations, and Brainworks (questions involving higher order thinking or an open-ended approach to problems).
4. Each chapter is followed by a review exercise, an Extend Your Learning Curve activity to encourage students to explore mathematical concepts further or apply mathematics in real-life situations, and some questions requiring sentence or paragraph answers to encourage students to reflect on their learning experiences.
5. The right margins contain remarks on important information, concepts or definitions covered earlier related to the current material to help students recall them, discussion questions, interesting puzzles or facts that are related to mathematics, and some website references.
6. A list of general processes and heuristics for problem-solving is provided after the last chapter in each book, with worked examples using concepts pertinent to the material covered in the book. 

Discovering Mathematics Textbook 3B

Chapter 7      Trigonometry                                                                                                                   1

         7.1        Trigonometric Ratios Of Acute Angles                                                                                   2

                             A. Definition                                                                                                                       2

                             B. Values of Trigonometric Ratios                                                                           3

                             C. Applications to Right-angled Triangles                                                                5

         7.2        Trigonometric Ratios Of Obtuse Angles                                                                      13

         7.3        Formula For The Area Of A Triangle                                                                           18

         7.4        The Sine Rule                25

                             A. Case of Two Angles and A Side                                                                       26

                             B. Case of Two Sides and A Non-included Angle                                                 26

         7.5        The Cosine Rule    32

Chapter 8 Applications of trigonometry                                                                                               45

         8.1        Bearing Problems                                                                                                          46

         8.2        Angles Of Elevation And Depression                                                                            53

         8.3        Simple Three-Dimensional Problems                                                                           57

        In A Nutshell                                                                                                                                           64

Chapter 9      Coordinate Geometry                                                                                                     72

         9.1        Length Of A Line Segment                                                                                            73

         9.2        Gradient O f A StraightLine                                                                                           79

         9.3        Equation Of A StraightLine                                                                                            84

Chapter 10    Arc Lengths And sector Areas                                                                                       95

         10.1      Arc Lengths                                                                                                                    96

         10.2      Sector Areas And Segment Areas                                                                               102

         10.3      Radian Measure                                                                                                           107

                             A. Definition                                                                                                            107

                             B. Conversion between Radians and Degrees                                                      108

         10.4      Formulae In Radian Measure                                                                                      113

Chapter 11 Quartiles And Percentiles                                                                                                125

         11.1      Cumulative Frequency Diagrams                                                                                126

         11.2      Range, Quartiles, Interquartile Range And Percentiles                                               134

                             A. Range                                                                                                                134

                             B. Quartiles and Interquartile Range                                                                      135

                             C. Percentiles                                                                                                         142

         11.3      Box-And-Whisker Plots                                                                                                147

Problem-solving Processes and Heuristics                                                                                        163

Answers                                                                                                                                              169