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Plane Trigonometry
 Use of Subsidiary Angles
 Sources and References

Plane Trigonometry

Use of Subsidiary Angles

749 To adapt π‘ŽΒ±π‘ to logarithmic computation. Take πœƒ=tanβˆ’1π‘π‘Ž then π‘Ž+𝑏=π‘Žsec2πœƒ 750 For π‘Žβˆ’π‘=π‘Ž2cos(πœƒ+45Β°)cosπœƒ 751 To adapt π‘Žcos𝐢±𝑏sin𝐢 to logarithmic computation. Take πœƒ=tanβˆ’1π‘Žπ‘, then π‘Žcos𝐢±𝑏sin𝐢=(π‘Ž2+𝑏2)sin(πœƒΒ±πΆ)By 617 For similar instances of the use of a subsidiary angle, see (726) to (730). 752 To solve a quadratic equation by employing a subsidiary angle. If π‘₯2βˆ’2𝑝π‘₯+π‘ž=0 be the equation, π‘₯=𝑝1Β±1βˆ’π‘žπ‘2By 45 Case I. If π‘ž be <𝑝2, put π‘žπ‘2=sin2πœƒ; then π‘₯=2𝑝cos2πœƒ2, and 2𝑝sin2πœƒ2By 639, 640 Case II. If π‘ž be >𝑝2, put π‘žπ‘2=sec2πœƒ; then π‘₯=𝑝(1±𝑖tanπœƒ), imaginary roots614 Case III. If π‘ž be negative, put π‘žπ‘2=tan2πœƒ; then π‘₯=π‘žcotπœƒ2, and π‘₯=βˆ’π‘žcotπœƒ2By 644, 645

Sources and References

https://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive

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References

  1. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science &amp; Engineering
  2. Ayres, F. JR, Moyer, R.E., 1999, Schaum's Outlines: Trigonometry
  3. Hopkings, W., 1833, Elements of Trigonometry
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