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Life of Fred: Trigonometry Expanded Edition


After Beginning Algebra, Advanced Algebra and Geometry, this book completes everything you need for calculus. Angles of elevation, Definition of the sine function, Angles of depression, Area of a triangle = ½ab sin θ, Heron’s formula, Review of graphing and significant digits, Discrete and continuous variables as illustrated in The Merchant of Venice, Tangent function, Why we create new mathematics, Limit of tan θ as θ approaches 90º, Ordinal and cardinal numbers, Cosine function, Graphing y = sin x, Identity function, Contrapositives, Domain and range of a function, Defining 6 to the pi power, Trig angles in standard position, Expanding the domain of a function, Periodic functions, Identities from algebra, Even and odd functions, Trig identities for sine and cosine, for tangent, for secant, Four suggestions for increasing success in solving trig identities, Trig identities for cotangent and cosecant, Nine tricks for solving trig identities, Shortcuts for graphing y = a sin (bx + c), Degrees, minutes, and seconds, Conversion factors, Radians, Videlicet, exempli. gratia, and id est, Area of a segment of a circle, Solving conditional trig equations, Related angles, Joseph Lister, Multiple angle formulas and their proofs, Symmetric law of equality, Probability of finding a right triangle, Law of Cosines, Florence Nightingale, Law of Sines, Inverse functions, One-to-one functions, Hyperbole, Principal values of the inverse trig functions, Ambiguous case for the law of sines, Why sin (2 Arctan 3) equals 3/5, Polar coordinates, Graphing a cardioid and a lemniscate, Codomain of a function, Official definition of the number one, Proof that the square root of 2 is irrational, Transcendental numbers, Complex numbers, Russell’s paradox, Malfatti’s problem and its solution in 1967, r cis θ, de Moivre’s theorem and its proof, The millionth roots of i, Review of the major parts of high school algebra and a preview of all of Calculus.