 | John Farrar - Logarithms - 1822 - 244 pages
...the chords of b, c, respectively. From a known theorem of spherical tigonometry (Trig. 53), we have cos a = cos 6 cos c + sin b sin c cos A. But cos c = (cos I c)1 — (sin | c)2 (Trig. 11), = i — (sin | c)2 — (sin | c)2 (Trig. 10), = 1... | |
 | Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...-\- B + C0> exceeding a quadrant has its cosine negative.* 3. The expressions of art. 53 give also, cos a — cos 6 cos c = sin b sin c cos A , cos b — cos a cos c — sin a sin c cos B ; t In art 27, the equation cos 6' — cos a' _ tang... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...each station ? SECTION V. Show that 1. Log MN = log M + log N. 2. Show that in any spherical triangle cos a = cos 6 cos c + sin b sin c cos A. 3. Determine sin A from the above formula, under a DIFFERENTIAL AND INTEGRAL CALCULUS. SECTION I. 1... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...cosines of those angles. 1. The first and second of equations (1) give, after transposing the terms, cos a — cos 6 cos c = sin b sin c cos A, cos b — cos a cos c = sin a sin c cos B; by adding, we have, cos a + cos 6 — cos c (cos a •J-... | |
 | Isaac Todhunter - Spherical trigonometry - 1859 - 156 pages
...thus sin FED is still equal to sin B. 43. To prove that cot a sin 6 = cot A sin C + cos b cos C. Ve cos a = cos 6 cos c + sin b sin c cos A, cos c = cos a cos b + sin a sin b cos C, sin C Substitute the values of cos c and sin c in the first... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...that we have two admissible values for C, if <£ + a is less than IT, and <f> - a is positive. And cos a, = cos 6 cos c + sin b sin c cos A = cos b (cos c + sin c tan b cos A) ; assume tan 6 = tan 6 cos A ; thus i / - , m cos b cos (c - 6)... | |
 | William Chauvenet - Trigonometry - 1924 - 268 pages
...to AB'O, we have »-a) = cos6cos(180°-c)+sin6sin(180°-c)cos(180°— ¿) or by PI. Trig. (64), — cos a = — cos 6 cos c — sin b sin c cos A and changing all the signs cos a = cos b cos c + sin b sin c cos A the same result that would have... | |
 | Mathematics - 1881 - 608 pages
...sin26 sin'c 1 — cos a cos 6 cos c* The proof is very simple; from the usual formulae we have cos'a = cos a cos 6 cos c + sin b sin c cos A cos a ; adding sin'a and transposing, 1 — cos a cos b cos c = sin' a + sin b sin c cos A cos a; (1)... | |
 | Webster Wells - 1883 - 298 pages
...5) sin c cos (180° — A) ' or (Art. 43) , — cosa= (—cos6) cos c + sin b sine (— cos.4) That is, cos a = cos 6 cos c + sin b sin c cos A Similarly, we may prove the theorem when b is less than 90°, and c greater than 90°. CA8E III. When... | |
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C are the angles opposite these sides the three equations cos a = cos 6 cos c + sin b sin c cos A... 
