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Plane Trigonometry
 Properties of The Triangle
  Proof
 Sources and References

Plane Trigonometry

Properties of The Triangle

image 700 𝑐=π‘Žcos𝐡+𝑏cos𝐴 701 π‘Žsin𝐴=𝑏sin𝐡=𝑐sin𝐢 702 π‘Ž2=𝑏2+𝑐2βˆ’2𝑏𝑐cos𝐴

Proof

By Euc. I. 12 and 13, π‘Ž2=𝑏2+𝑐2βˆ’2𝑐.𝐴𝐷. 703 cos𝐴=𝑏2+𝑐2βˆ’π‘Ž22𝑏𝑐 704 If π‘ β‰‘π‘Ž+𝑏+𝑐2, and β–³ denote the area 𝐴𝐡𝐢, sin𝐴2=(π‘ βˆ’π‘)(π‘ βˆ’π‘)𝑏𝑐, cos𝐴2=𝑠(π‘ βˆ’π‘Ž)𝑏𝑐641, 642, 703, 9, 10, 1 705 tan𝐴2=(π‘ βˆ’π‘)(π‘ βˆ’π‘)𝑠(π‘ βˆ’π‘Ž) 706 sin𝐴=2𝑏𝑐𝑠(π‘ βˆ’π‘Ž)(π‘ βˆ’π‘)(π‘ βˆ’π‘) 707 β–³=𝑏𝑐2sin𝐴=𝑠(π‘ βˆ’π‘Ž)(π‘ βˆ’π‘)(π‘ βˆ’π‘)707, 706 708 β–³=142𝑏2𝑐2+𝑐2π‘Ž2+π‘Ž2𝑏2βˆ’π‘Ž4βˆ’π‘4βˆ’π‘4

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 & Engineering
  2. Ayres, F. JR, Moyer, R.E., 1999, Schaum's Outlines: Trigonometry
  3. Hopkings, W., 1833, Elements of Trigonometry
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