Plane trigonometry / Fred W. Sparks and Paul K. Rees.
Series Prentice-Hall mathematics seriesEditor: Englewood Cliffs, N.J. : Prentice-Hall, 1965Edición: 5th edDescripción: ix, 230, 76 p. : il. ; 24 cmOtro título: Plane trigonometry : with tablesOtra clasificación: 26Incluye: Logarithmic and trigonometric tables. 1 THE TRIGONOMETRIC FUNCTIONS, [1] 1.1. Introduction, [1.] 1.2. The real number system, [2.] 1.3. Directed line segments, [5.] 1.4. Positive and negative angles, [6.] 1.5. The rectangular cartesian coordinate system, [7.] 1.6. The relation between the abscissa, ordinate, and radius vector, [8.] 1.7. Variables and functions, [11.] 1.8. Definition of the trigonometric functions of an angle, [12.] 1.9. Algebraic signs of the trigonometric functions, [15.] 1.10. Values of the other trigonometric functions when one is given, [15.] 1.11. Values of the trigonometric functions of 30°, 45°, and their multiples, [19.] 1.12. Functions of quadrantal angles, [21.] 2 SOLUTION OF RIGHT TRIANGLES, [25] 2.1. Introduction, [25.] 2.2. Significant figures, [27.] 2.3. Calculations involving approximate or measured quantities, [28.] 2.4. Tables of values of the trigonometric functions, [31.] 2.5. Given an angle; to find the values of its functions, [31.] 2.6. Given the value of a function: to find the corresponding angle, [32.] 2.7. Interpolation, [32.] 2.8. Trigonometric functions of an acute angle of a righttriangle, [37.] 2.9. The solution of right triangles, [38.] 2.10. Angles of elevation and depression, [43.] 2.11. The direction of a line, [45.] 2.12. Vectors, [46.] 3 FUNDAMENTAL IDENTITIES, [54] 3.1. Introduction, [54.] 3.2. Reciprocal functions, [55.] 3.3. Ratio relations, [55.] 3.4. Pythagorean identities, [56.] 3.5. Fundamental identities, [56.] 3.6. Trigonometric reductions, [57.] 3.7. Identities, [58.] 4 TRIGONOMETRIC REDUCTIONS, [65] 4.1. The related angle, [65.] 4.2. Functions of negative angles, [69.] 5 RADIAN MEASURE AND FUNCTIONS OF NUMBERS, [72] 5.1. Functions of radians and numbers, [72.] 5.2. The relation between degrees and radians, [74.] 5.3. The central angle and arc length, [77.] 5.4. Angular speed and linear speed, [78.] 6 VARIATION AND GRAPHS OF THE TRIGONOMETRIC FUNCTIONS, [82] 6.1. Introduction, [82.] 6.2. Variation of the sine, cosine, and tangent, [83.] 6.3. Periodic functions, [84.] 6.4. Bounds and amplitude, [85.] 6.5. The graph of Y — sin 0, [86.] 6.6. The graph of Y — cos 0, [87.] 6.7. The graph of Y = tan Ɵ, [87.] 6.8. Graphs of the other trigonometric functions, [89.] 6.9. A constant times a function of b0 c, [91.] 6.10. Composition of ordinates, [92.] 7 FUNCTIONS OF A COMPOSITE ANGLE, [95] 7.1. Introduction, [95.] 7.2. The distance formula, [96.] 7.3. The cosine of the sum of two angles, [97.] 7.4. The cosine of twice an angle, [98.] 7.5. The cosine of half an angle, [99.] 7.6. The cosine of the difference of two angles, [99.] 7.7. An application, [100.] 7.8. Functions of π / 2 — C, [102.] 7.9. The sine of the sum of two angles, [103.] 7.10. The sine of twice an angle, [103.] 7.11. The sine of half an angle, [103.] 7.12. The sine of the difference of two angles, [104.] 7.13. The tangent of the sum of two angles, [106.] 7.14. The tangent of twice an angle, [107.] 7.15. The tangent of half an angle, [107.] 7.16. The tangent of the difference of two angles, [108.] 7.17. An application needed in analytic geometry, [108.] 7.18. The product and factor formulas, [111.] 7.19. Summary of formulas, [113.] 8 LOGARITHMS, [117] 8.1 Introduction, [117.] 8.2. Definition and laws of exponents, [118.] 8.3. Definition of a logarithm, [119.] 8.4. Properties of logarithms, [120.] 8.5. The common, or the Briggs, system of logarithms, [122.] 8.6. Given log N, to find N, [126.] 8.7. Logarithmic computation, [127.] 9 LOGARITHMIC SOLUTION OF TRIANGLES, [132] 9.1. Logarithms of the trigonometric functions, [132.] 9.2. Logarithmic solution of right triangles, [134.] 9.3. Oblique triangles, 113. 9.4. The law of sines, [136.] 9.5. The area of a triangle, [137.] 9.6. Case A, [138.] 9.7. Case B—the ambiguous case, [141.] 9.8. The law of cosines, [148.] 9.9. The law of tangents, [152.] 9.10. Illustrative example for Case C, [153.] 9.11. The half-angle formulas, [156.] 9.12. Illustrative example for Case D, [158.] 10 TRIGONOMETRIC EQUATIONS, [166] 10.1. Introduction, [166.] 10.2. Equations that contain only one function and only one angle, [167.] 10.3. Equations with one member zero and the other factorable, [168.] 10.4. Equations reducible to a form solvable by factoring, [170.] 10.5. Equations of the form A sin Ɵ + B cos Ɵ — C, [171.] 11 THE INVERSE TRIGONOMETRIC FUNCTIONS, [175] 11.1. The inverse of a function, [175.] 11.2. The inverse trigonometric functions, [176.] 11.3. Graphs of the inverse trigonometric functions, [177.] 11.4. Transformation of inverse trigonometric functions, [179.] 11.5. Inverse trigonometric identities, [183.] 12 COMPLEX NUMBERS, [188] 12.1. Introduction, [188.] 12.2. Equal complex numbers; conjugate complex numbers, [189.] 12.3. Graphical representation, [189.] 12.4. Algebraic addition and subtraction, [191.] 12.5. Geometric addition and subtraction, [191.] 12.6. Algebraic multiplication and division, [192.] 12.7. Trigonometric representation, [193.] 12.8. The product of two complex numbers, [194.] 12.9. The quotient of two complex numbers, [195.] 12.10. Demoivre’s theorem, [197.] 12.11. Roots of complex numbers, [197.] 13 POLAR COORDINATES, [201] 13.1. Some definitions and concepts, [201.] 13.2. Pairs of coordinates for a point, [202.] 13.3. Symmetry and intercepts, [203.] 13.4. Construction of the graph, [206.] 13.5. Relations between rectangular and polar coordinates, [210.] APPENDIX MOLLWEIDE’S EQUATIONS, [213] ANSWERS, [215] INDEX, [227]
"Contains approximately 1900 problems in 39 exercises"--Preface.
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Incluye: Logarithmic and trigonometric tables.
1 THE TRIGONOMETRIC FUNCTIONS, [1] --
1.1. Introduction, [1.] --
1.2. The real number system, [2.] --
1.3. Directed line segments, [5.] --
1.4. Positive and negative angles, [6.] --
1.5. The rectangular cartesian coordinate system, [7.] --
1.6. The relation between the abscissa, ordinate, and radius vector, [8.] --
1.7. Variables and functions, [11.] --
1.8. Definition of the trigonometric functions of an angle, [12.] --
1.9. Algebraic signs of the trigonometric functions, [15.] --
1.10. Values of the other trigonometric functions when one is given, [15.] --
1.11. Values of the trigonometric functions of 30°, 45°, and their multiples, [19.] --
1.12. Functions of quadrantal angles, [21.] --
2 SOLUTION OF RIGHT TRIANGLES, [25] --
2.1. Introduction, [25.] --
2.2. Significant figures, [27.] --
2.3. Calculations involving approximate or measured quantities, [28.] --
2.4. Tables of values of the trigonometric functions, [31.] --
2.5. Given an angle; to find the values of its functions, [31.] --
2.6. Given the value of a function: to find the corresponding angle, [32.] --
2.7. Interpolation, [32.] --
2.8. Trigonometric functions of an acute angle of a righttriangle, [37.] --
2.9. The solution of right triangles, [38.] --
2.10. Angles of elevation and depression, [43.] --
2.11. The direction of a line, [45.] --
2.12. Vectors, [46.] --
3 FUNDAMENTAL IDENTITIES, [54] --
3.1. Introduction, [54.] --
3.2. Reciprocal functions, [55.] --
3.3. Ratio relations, [55.] --
3.4. Pythagorean identities, [56.] --
3.5. Fundamental identities, [56.] --
3.6. Trigonometric reductions, [57.] --
3.7. Identities, [58.] --
4 TRIGONOMETRIC REDUCTIONS, [65] --
4.1. The related angle, [65.] --
4.2. Functions of negative angles, [69.] --
5 RADIAN MEASURE AND FUNCTIONS OF NUMBERS, [72] --
5.1. Functions of radians and numbers, [72.] --
5.2. The relation between degrees and radians, [74.] --
5.3. The central angle and arc length, [77.] --
5.4. Angular speed and linear speed, [78.] --
6 VARIATION AND GRAPHS OF THE TRIGONOMETRIC FUNCTIONS, [82] --
6.1. Introduction, [82.] --
6.2. Variation of the sine, cosine, and tangent, [83.] --
6.3. Periodic functions, [84.] --
6.4. Bounds and amplitude, [85.] --
6.5. The graph of Y — sin 0, [86.] --
6.6. The graph of Y — cos 0, [87.] --
6.7. The graph of Y = tan Ɵ, [87.] --
6.8. Graphs of the other trigonometric functions, [89.] --
6.9. A constant times a function of b0 c, [91.] --
6.10. Composition of ordinates, [92.] --
7 FUNCTIONS OF A COMPOSITE ANGLE, [95] --
7.1. Introduction, [95.] --
7.2. The distance formula, [96.] --
7.3. The cosine of the sum of two angles, [97.] --
7.4. The cosine of twice an angle, [98.] --
7.5. The cosine of half an angle, [99.] --
7.6. The cosine of the difference of two angles, [99.] --
7.7. An application, [100.] --
7.8. Functions of π / 2 — C, [102.] --
7.9. The sine of the sum of two angles, [103.] --
7.10. The sine of twice an angle, [103.] --
7.11. The sine of half an angle, [103.] --
7.12. The sine of the difference of two angles, [104.] --
7.13. The tangent of the sum of two angles, [106.] --
7.14. The tangent of twice an angle, [107.] --
7.15. The tangent of half an angle, [107.] --
7.16. The tangent of the difference of two angles, [108.] --
7.17. An application needed in analytic geometry, [108.] --
7.18. The product and factor formulas, [111.] --
7.19. Summary of formulas, [113.] --
8 LOGARITHMS, [117] --
8.1 Introduction, [117.] --
8.2. Definition and laws of exponents, [118.] --
8.3. Definition of a logarithm, [119.] --
8.4. Properties of logarithms, [120.] --
8.5. The common, or the Briggs, system of logarithms, [122.] --
8.6. Given log N, to find N, [126.] --
8.7. Logarithmic computation, [127.] --
9 LOGARITHMIC SOLUTION OF TRIANGLES, [132] --
9.1. Logarithms of the trigonometric functions, [132.] --
9.2. Logarithmic solution of right triangles, [134.] --
9.3. Oblique triangles, 113. 9.4. The law of sines, [136.] --
9.5. The area of a triangle, [137.] --
9.6. Case A, [138.] --
9.7. Case B—the ambiguous case, [141.] --
9.8. The law of cosines, [148.] --
9.9. The law of tangents, [152.] --
9.10. Illustrative example for Case C, [153.] --
9.11. The half-angle formulas, [156.] --
9.12. Illustrative example for Case D, [158.] --
10 TRIGONOMETRIC EQUATIONS, [166] --
10.1. Introduction, [166.] --
10.2. Equations that contain only one function and only one angle, [167.] --
10.3. Equations with one member zero and the other factorable, [168.] --
10.4. Equations reducible to a form solvable by factoring, [170.] --
10.5. Equations of the form A sin Ɵ + B cos Ɵ — C, [171.] --
11 THE INVERSE TRIGONOMETRIC FUNCTIONS, [175] --
11.1. The inverse of a function, [175.] --
11.2. The inverse trigonometric functions, [176.] --
11.3. Graphs of the inverse trigonometric functions, [177.] --
11.4. Transformation of inverse trigonometric functions, [179.] --
11.5. Inverse trigonometric identities, [183.] --
12 COMPLEX NUMBERS, [188] --
12.1. Introduction, [188.] --
12.2. Equal complex numbers; conjugate complex numbers, [189.] --
12.3. Graphical representation, [189.] --
12.4. Algebraic addition and subtraction, [191.] --
12.5. Geometric addition and subtraction, [191.] --
12.6. Algebraic multiplication and division, [192.] --
12.7. Trigonometric representation, [193.] --
12.8. The product of two complex numbers, [194.] --
12.9. The quotient of two complex numbers, [195.] --
12.10. Demoivre’s theorem, [197.] --
12.11. Roots of complex numbers, [197.] --
13 POLAR COORDINATES, [201] --
13.1. Some definitions and concepts, [201.] --
13.2. Pairs of coordinates for a point, [202.] --
13.3. Symmetry and intercepts, [203.] --
13.4. Construction of the graph, [206.] --
13.5. Relations between rectangular and polar coordinates, [210.] --
APPENDIX MOLLWEIDE’S EQUATIONS, [213] --
ANSWERS, [215] --
INDEX, [227] --
"Contains approximately 1900 problems in 39 exercises"--Preface.
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