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SOURCE: Pease E., Wadsworth G. Engineering Trigonometry 1946
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MEDIAINFO
Textbook in PDF format This volume is also written without presupposing any particular knowledge on the part of the student of any portion of this subject. Advanced methods are used whenever it seems advisable. But the advanced methods, as such, are so selected that they are no harder for the student to learn than the so-called elementary ones. These advanced methods merely enable the student to compress the mathematical shorthand to the point where a problem normally containing many steps appears to contain few steps, thus permitting the student to get a clearer bird’s-eye view of the problem as a whole. Students frequently fail to complete a problem merely because the particular problem considered involves a large number of individual steps which cannot be separately appreciated until a vision of the entire process is attained. Advanced methods only will assist the student in this dilemma. Any development of student ability to go from the physical situation to the mathematical representation, or ability to interpret the revamped equation back into new physical significance, will result in the narrowing of the present gap between the assimilation of the mathematical approaches and the applying of these approaches in succeeding courses. Trigonometry Defined Vocabulary BuildUp Scope of Trigonometry Some Prerequisites to the Study of Trigonometry Trigonometric Functions Right Triangles Definitions and Interrelations of the Trigonometric Functions of an Angle Numerical Values of the Trigonometric Ratios for the Special Angles 30o, 45o, 60o and Multiples of 90о General Procedure for Solving a Right Triangle Method of Obtaining the Trigonometric Ratios Determination of Any Trigonometric Ratio for Any Angle Graphical Representation of Principal Trigonometric Ratios Engineering on Preceding Chapters Problems From Electrical Engineering Solution of Right Triangles in Electrical Engineering Problems From Applied Mechanics Problem From Surveying Logarithms Significance of a Logarithm Characteristic and Mantissa of a Logarithm Operations That May Be Simplified by Logarithms Subtraction of a Large Logarithm from a Small Logarithm Use of Logarithms Decimal Power Logarithm Tables Arrangement Functions The Natural System of Logarithms, for Which Base = e = 2. 71828… Arrangement and Use of Typical of Natural Logarithms Illustrative Problems Using Common or Briggs Logarithms (Base = 10 ) Cologarithms Illustrative Problems Involving Natural Logarithms Change of Bases; Relation Between Common and Natural Logarithms Stationary Adjacent Scales and Slide Rules Use of Stationary Adjacent Scales and Slide Rules Illustrative Problems on Construction and Use of Stationary Adjacent Scales Use of Slide Rule for Multiplication and Division Illustrative Problems on Construction and Use of Sliding Scales in General Illustrative Examples on Folded and Inverted Scales Practice in Use of K, T, and S Scales Additional Illustrative Slide Rule Examples Construction and Use of a Slide Rule Designed for a Particular Formula Trigonometric Relations and Identities Some Other Interrelations Between the Trigonometric Ratios Identities Formulas for sin (x÷y) and cos (x+y) Formulas for tan (x+y) and cot (x+y) Functions of (x —y) Formulas for Double Angle The “HalfAngle Formulas Product to Sum Formulas Sum to Product Formulas Complex Numbers Imaginary Numbers Operations With Imaginary Numbers Complex Numbers; Visualization of Imaginary Numbers Multiplication and Division of Complex Numbers Representation of Complex Number in Polar Coordinates Multiplication of Complex Numbers in Polar Form Division of Complex Numbers in Polar Form Engineering Illustratives on Multiplication and Division of Complex Numbers DeMoivre, s Theorem Infinite Series for sin a and cos a Complex Numbers and Trigonometric Functions in Terms of e Hyperbolic Functions Oblique Triangles Definition of Oblique Triangle Methods of Solving Oblique Triangles Law of Sines Law of Cosines Law of Tangents Area of Triangle in Terms of Sides by Heron’s Formula Radius of Inscribed Circle in Terms of Sides of Triangle Formulas for Tangents of HalfAngles in Terms of Sides Discussion of Type IV Solution of Triangles of Type IV Inverse Functions InverseFunction Notation MultipleValuedness of an Inverse Function; Principal Values Inverse Hyperbolic Functions Process of Inversion Graphs Inversion With Respect to the Unit Circle Use of Process of Inversion in Drawing Graphs A Circle Inverts Into a Circle Graphical Process of Inversion for Reciprocal of a Complex Number Engineering of Process of Inversion Oblique Triangles Solved By Complex Numbers Derivation of Law of Sines by Complex Numbers Solution of Triangle of Type I (Given One Side and Two Angles) by Complex Numbers ComplexNumber Investigation of Triangle of Type II (Given Two Sides and Included Angle) ComplexNumber Investigation of Triangle of Type III (Given Three Sides) ComplexNumber Investigation of Triangle of Type IV (Given Two Sides and the Angle Opposite One of Them) Summary of Investigations of Triangles of the Four Types Approximate Number Computations Exact, Approximate, and Round Numbers Significant figures Absolute Error and Relative Error Rounding off Numbers Sum of Approximate Numbers Sum of Approximate Numbers With Limit on Relative Error Correctness of Round Numbers Sum of Approximate Numbers That Is to Be Correct to a Particular Place Product of an Exact Factor and an Approximate Factor That Is to Be in Error by not More Than One Unit in a Particular Place Product of an Exact Factor and an Approximate Factor With a PreStated Limit of Relative Error Product of Two Approximate Factors That Is to Be in Error by not More Than One Unit in a Particular Place Additional Discussion Product of Two Exact Factors With a PreStated Relative Error Product of Two or More Factors With a PreStated Limit of Relative Error Relation Among Numbers of Significant Figures in Dividend, Divisor, and Quotient Approximations in Given Parts of Triangles Right Spherical Triangles Geometric Properties of General Spherical Triangle Limiting Conditions Classes of Right Spherical Triangles Polar Triangle; Quadrantal Triangle Ten Formulas and Three Theorems for Solving Right Spherical Triangles Illustrative Problems on Solutions of Right Spherical Triangles Terrestrial Triangles Celestial Triangles Oblique Spherical Triangles Law of Sines Law of Cosines for Sides Law of Cosines for Angles Classification of Spherical Triangles Solution of Class I Triangles by Tangent HalfAngle Method Solution of Class II Triangles by Tangent HalfSide Method Solution of Triangles of Classes III and IV by Napier’s Analogies How to Visualize a Spherical Triangle from Given Values Solution of Triangles of Classes V and VI by Simultaneous Laws Navigation Time and Point of the Horizon at Which the Sun Rises on a Specified Date Difference Between True Solar Time and Mean Solar Time; Equation of Time Sidereal Time; Conversion of Greenwich Civil Time to Greenwich Sidereal Time The “Time Sight” Checking of Latitude Graphical Process for Determining Latitude and Longitude Determination of the Coordinates (Greenwich Hour Angle and Declination) of a Subsolar Point Construction of a Mercator Chart Dead Reckoning Position (DRP) and Sumner Line Determination of Observer’s Latitude and Longitude Without Plotting Subcelestial Points Appendix Recapitulation of Formulas Derivations of Ten Formulas For Right Spherical Triangles Instructions For Use of Tables Common logarithms Natural trigonometric functions Logarithms of trigonometric functions Natural logarithms Radian measure Powers, roots, reciprocals Powers of e and hyperbolic functions Haversines and their logarithms Tables Mantissas of Common Logarithms Natural Trigonometric Functions Sines and Cosines Tangents and Cotangents Logarithmic Trigonometric Functions Natural Logarithms Radian Measure Degrees to radians Functions of angles in radians Radians to degrees Powers, Roots, Reciprocals Powers of “e” and Hyperbolic Functions Haversines
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