Life of Fred: Trigonometry (Expanded Edition)

After Beginning Algebra, Advanced Algebra and Geometry, this book completes everything you need for calculus. Review of the major parts of high school algebra and a preview of all of Calculus.

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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.

This book has all the problems completely worked out, which wasn’t true in the old books.

Click here to view a sample lesson
(Opens in a new window or tab)