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1 Historical background Introduction. What is trigonometry? The origins of trigonometry |
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1 | (4) |
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2 The tangent Introduction. The idea of the tangent ratio. A definition of tangent. Values of the tangent. Notation for angles and sides. Using tangents. Opposite and adjacent sides |
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5 | (13) |
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3 Sine and cosine Introduction. Definition of sine and cosine. Using the sine and cosine. Trigonometric ratios of 45(Degree), 30(Degree) and 60(Degree). Using the calculator accurately. Slope and gradient. Projections. Multistage problems |
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18 | (18) |
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4 In three dimensions Introduction. Pyramid problems. Box problems. Wedge problems |
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36 | (10) |
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5 Angles of any magnitude Introduction. Sine and cosine for any angle. Graphs of sine and cosine functions. The tangent of any angle. Graph of the tangent function. Sine, cosine and tangent |
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46 | (8) |
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6 Solving simple equations Introduction. Solving equations involving sines. Solving equations involving cosines. Solving equations involving tangents |
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54 | (9) |
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7 The since and cosine formulae Notation. Area of a triangle. The sine formula for a triangle. The ambiguous case. The cosine formula for a triangle. Introduction to surveying. Finding the height of a distant object. Distance of an inaccessib le object. Distance between two inaccessible but visible objects. Triangulation |
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63 | (22) |
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8 Radians Introduction. Radians. Length of a circular arc. Converting from radians to degrees. Area of a circular sector |
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85 | (7) |
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9 Relations between the ratios Introduction. Secant, cosecant and cotangent |
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92 | (6) |
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10 Ratios of compound angles Compound angles. Formulae for sin(A + B) and sin(A - B). Formulae for cos(A + B) and cos(A - B). Formulae for tan(A + B) and tan (A - B). Worked examples. Multiple angle formulae. Identities. More trigonometric equations. |
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98 | (15) |
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11 The form a sin x + b cos x Introduction. The form y = a sin x + b cos x. Using the alternative form |
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113 | (8) |
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12 The factor formulae The first set of factor formulae. The second set of factor formulae |
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121 | (8) |
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13 Circles related to a triangle The circumcircle. The incircle. The encircles. Heron's formula: the area of a triangle |
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129 | (12) |
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14 General solution of equations The equation sin Theta = sin Alpha. The equation cos Theta = cos Alpha. The equation tan Theta = tan Alpha. Summary of results |
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141 | (9) |
| Glossary |
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150 | (3) |
| Summary of trigonometric formulae |
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153 | (4) |
| Answers |
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157 | (14) |
| Index |
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171 | |
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