Plane And Spherical Trigonometry
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From Art. 119, we have cos a = cos b cos c + sin b sin c cos a.
Therefore cos « = cos n ,~ cos h cos c . (1) sin b sin c But 2 sin 2 1« = 1- cos a _ sin b sin c - - cos a -f- cos b cos c sin b sin c _ cos a — cos (b — c) sin b sin c Applying formula (4) of Art. 73, we have _ sin j- (a + b — c) sin | (a — 5 + c) sin 2 I a = ?rT " — w olxl * sin 6 sin c Letting 2 .9 = a + 6 + c, we have sin 1 q -^f S in ( J - 6 ^ Sln ( S ~ C ) • (2) sin 6 sin c 125 126 TRIGONOMETRY Similarly uniting (1) with 2 co...s 2 }« = 1+ cos a, sin b sin c -f cos a — cos b cos c we have 2 cos 2 4- « sin b sin c cos (6 + c) — cos a sin 6 sin c 2 sin i. (q + 6 -f c) sin -j- (— a +& +c) sin b sin c Therefore cos | a = ^^J^ZZ*! . ( 3 ) * sin 6 sin c Uniting (2) and (3), tan 4 a=-\/ sin r * ~ 6) sin (j? ~ C) = tan r (4) * sin 5 sin (s — a) sin (5 — a) Similarly tan|p = ^| sin '^^ ($ ~ ^ = _ i _ ta ° / - 1 , sin 5 sin (s — b) sin {s — by (s — a) sin (s — b) _ tan r sin 5 (sin s — c) sin (5 — c) and tan I , = /sin (s -Q sin (s - 6) = tan r * sin 5 (sin 5 — c) sin (5 — ^ where tan r = / sin (8 - q) sin (.9 - b) sm> - c) .
What to read after Plane And Spherical Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by Bauer, George N. (George Neander), B. 1872 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
From Art. 119, we have cos a = cos b cos c + sin b sin c cos a.
Therefore cos « = cos n ,~ cos h cos c . (1) sin b sin c But 2 sin 2 1« = 1- cos a _ sin b sin c - - cos a -f- cos b cos c sin b sin c _ cos a — cos (b — c) sin b sin c Applying formula (4) of Art. 73, we have _ sin j- (a + b — c) sin | (a — 5 + c) sin 2 I a = ?rT " — w olxl * sin 6 sin c Letting 2 .9 = a + 6 + c, we have sin 1 q -^f S in ( J - 6 ^ Sln ( S ~ C ) • (2) sin 6 sin c 125 126 TRIGONOMETRY Similarly uniting (1) with 2 co...s 2 }« = 1+ cos a, sin b sin c -f cos a — cos b cos c we have 2 cos 2 4- « sin b sin c cos (6 + c) — cos a sin 6 sin c 2 sin i. (q + 6 -f c) sin -j- (— a +& +c) sin b sin c Therefore cos | a = ^^J^ZZ*! . ( 3 ) * sin 6 sin c Uniting (2) and (3), tan 4 a=-\/ sin r * ~ 6) sin (j? ~ C) = tan r (4) * sin 5 sin (s — a) sin (5 — a) Similarly tan|p = ^| sin '^^ ($ ~ ^ = _ i _ ta ° / - 1 , sin 5 sin (s — b) sin {s — by (s — a) sin (s — b) _ tan r sin 5 (sin s — c) sin (5 — c) and tan I , = /sin (s -Q sin (s - 6) = tan r * sin 5 (sin 5 — c) sin (5 — ^ where tan r = / sin (8 - q) sin (.9 - b) sm> - c) .
What to read after Plane And Spherical Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by Bauer, George N. (George Neander), B. 1872 to read onlineMoreLess
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