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SOLUTION OF THE CUBIC EQUATION

23 + px + q=0,
BY TRIGONOMETRICAL TABLES.

Case L.
23 + px +9=0.

pp.
tan B =

= m.

= 8

tan A= tan : B. (1) x= F 2 cot 2 AV }p. (2) x=

=(+cot 2 A + cosec 2 AV-3)/ tp. (3) <=

- (+cot 2 A - - cosec 2 A V-3)/ }p.

2

Case II.
03 – px +q=0.

(m< 1.) sin B=m.

tan A=tan 4B. (1) x = F 2 cosec 2 AV {p. (2) x=(+ cosec 2 A + cot 2 AV-3)/ \ p. (3) x=(+ cosec 2 A cot 2 AV-3) }p.

=

(in > 1.)

Care III.
THE IRREDUCIBLE CASE.

23 – px +9=0.
cosec B=m.

A = { B.
(1) <= 2 sin AV Ip.
(2) x=+ 2 sin (60° – A) VIP.
(3) <= F 2 sin (60'+ A)/1p.

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