equation 7.53 eq:ana-cos-sin-series

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Supports

• depends_on lemma 7.73 $\cos 2 < 0$ ¶
  • depends_on definition 7.74 $\pi$ ¶
    • depends_on lemma 7.75 The first quadrant ¶
      • depends_on proposition 7.76 $\pi$ as the circle constant ¶
      • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶
        • depends_on lemma 7.78 Chord, arc, tangent ¶
        • depends_on proposition 7.85 Irrationality of $\pi$ ¶
        • depends_on proposition 7.79 The polygon recursion ¶
        • depends_on proposition 7.83 Viète's product ¶
        • depends_on proposition 125.2 Crystallographic restriction ¶
        • depends_on remark 7.88 $\pi$ elsewhere in this treatise ¶
      • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
    • depends_on proposition 7.76 $\pi$ as the circle constant ¶ ↺
    • depends_on proposition 7.79 The polygon recursion ¶ ↺
    • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶ ↺
    • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
• depends_on lemma 7.71 Derivatives; the Pythagorean identity ¶
  • depends_on lemma 7.75 The first quadrant ¶ ↺
  • depends_on lemma 7.78 Chord, arc, tangent ¶ ↺
  • depends_on lemma 9.136 Wallis integrals ¶
    • depends_on proposition 9.139 Series for the complete integral of the first kind ¶
      • depends_on proposition 9.144 The pendulum equation at finite amplitude ¶
  • depends_on proposition 7.76 $\pi$ as the circle constant ¶ ↺
  • depends_on proposition 7.85 Irrationality of $\pi$ ¶ ↺
  • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
  • depends_on proposition 9.141 First properties ¶
    • depends_on proposition 9.143 A cubic quadrature between two turning points ¶
    • depends_on proposition 9.142 The differential equation of the sine amplitude ¶
  • depends_on remark 7.80 Why these are the polygon perimeters ¶
• depends_on lemma 7.72 Addition theorems ¶
  • depends_on proposition 7.79 The polygon recursion ¶ ↺
  • depends_on proposition 7.77 Special values, periodicity, and the kernel ¶ ↺
  • depends_on proposition 7.83 Viète's product ¶ ↺
  • depends_on proposition 125.2 Crystallographic restriction ¶ ↺
  • depends_on remark 7.88 $\pi$ elsewhere in this treatise ¶ ↺
  • depends_on remark 7.80 Why these are the polygon perimeters ¶ ↺