# Trigonometry without tears

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• Publicado : 30 de noviembre de 2010

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Trig without Tears (Printer-Friendly Version)

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Trig without Tears
or, How to Remember Trigonometric Identities

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Contents

Trig without Tears Introduction About Trigonometry About Trigwithout Tears Bonus Topics What You Won’t Find Here Notation Interval Notation Degrees and Radians The Six Functions The Basic Two: Sine and Cosine Expressions for Lengths of Sides The Other Four: Tangent, Cotangent, Secant, Cosecant Six Functions in One Picture

23/04/2009

Trig without Tears (Printer-Friendly Version)

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Why Call ItSine? Functions of Special Angles Functions of 45° Functions of 30° and 60° Mnemonic for All Special Angles Functions of Any Angle Not Just Triangles Any More Why Bother? Reference Angles Signs of Function Values Examples: Function Values Identities for Related Angles Periodic Functions Solving Triangles Law of Sines Law of Cosines Detective Work: Solving All Types of Triangles The Cases Special Note:Side-Side-Angle Solving Triangles on the TI-83 or TI-84 The “Squared” Identities Sum and Difference Formulas Sine and Cosine of A±B Euler’s Formula Sine and Cosine of a Sum Sine and Cosine of a Difference Some Geometric Proofs Tangent of A±B Product-Sum Formulas Product to Sum Sum to Product Double Angle and Half Angle Formulas Sine or Cosine of a Double Angle Tangent of a Double Angle Sine orCosine of a Half Angle Tangent of a Half Angle Inverse Functions Principal Values Functions of Arcfunctions Example 1: cos(Arctan x) Example 2: cos(Arcsin x) Example 3: cos(Arctan 1/x)) Arcfunctions of Functions Example 4: Arccos(sin u) Example 5: Arcsec(cos u) Example 6: Arctan(sin u) Notes and Digressions

23/04/2009

Trig without Tears(Printer-Friendly Version)

Page 3 of 68

The Problem with Memorizing On the Other Hand ... Proof of Euler’s Formula Polar Form of a Complex Number Powers and Roots of a Complex Number Square Root of i Principal Root of Any Number Multiple Roots Logarithm of a Negative Number Cool Proof of Double-Angle Formulas Great Book on Problem Solving What’s New