 | Aaron Schuyler - Navigation - 1873 - 536 pages
...the angle, by the product of the sines of the adjacent sides. The first formula of article 136 gives, cos a — cos b cos c cos A = - : — : — -. -- sin b sin c Adding 1 to both members, we have, cos a + sin b sin c — cos b cos c 1 + COS A= - - : - 7 - : --... | |
 | Henry Nathan Wheeler - 1886 - 250 pages
...are real, ie that the quantity under the radical is in each case positive. § 21. From [12] we get cos A + cos B cos C cos a = : — — - — . sin B sin C Now proceeding as in § 20 and putting A+B+C=2S we get cos \ a = v/coB(SB)cog(S=C) V sin B sin C '... | |
 | Isaac Todhunter - Spherical trigonometry - 1879 - 176 pages
...a cos Ъ cos c), and this is equal to cos a sin B sin C sin2 a sin Ъ sin c, (Art. 41 ) ; therefore cos A + cos B cos C = cos a sin B sin C. Similarly the other two corresponding formulae may be proved. Thus the formulae in Art. 47 are established... | |
 | 1882 - 486 pages
...cot B — cot A _ sin A cos B cos 0 + sin B cos A cos C -f- sin C cos A cos B — sin A sin B sin C cos A cos B cos C — cos A sin B sin C — cos B sin A sin C — cos C sin A sin B Dividing both numerator and denominator by cos A cos B... | |
 | William John M'Clelland - 1885 - 182 pages
...Fundamental Formula (1) and (2). Let c = \. (1). Hence cos« = cos a cos b. (2). Again, from the formula, cos a — cos b cos c cos A = : — ; — ; . sin b sin c On substituting the value of cos a from Ex. (1) we have tan* cos A = . tone Similarly, tana cos B =... | |
 | Otto Rausenberger - Geometry - 1887 - 247 pages
...sämtliche acht Ecken , welche durch drei Ebenen bestimmt werden, gelten dieselben Sinusformeln. 5. Aus cos a — cos b cos c cos a = . , -•.sin b sin c folgt a T / 1 + cos « -i / sin b sin c + cos a — cos b cos c . a 4- fr + c . — a + fe sm — ^~... | |
 | 1891 - 718 pages
...A + B) = cos A cos B — sin A sin B, A + B being less than 90°. 11. Prove that cos ( A + B + C) = cos A cos B cos C — cos A sin B sin C — cos B sin G sin A — cos C sin A sin B. 4 cos (A + B — C) cos (A - B + C) cm(—A + B + C) =... | |
 | John Bascombe Lock - Logarithms - 1896 - 244 pages
...6 = cos c cos a + sin c sin a cos B, > (1) . , "cos c = cos a cos b + sin a sin b cos C. J Whence . cos a — cos b cos c cos A = ; ; , sin b sin c cos b — cos c cos a cosB = cos С — sm c sin a. cos c — cos a cos b f2) The last two formulae... | |
 | Frederick Anderegg, Edward Drake Roe - Trigonometry - 1896 - 136 pages
...Oblique Triangles. a. Formulas for Functions of i A, .! R, -', C. § 91. From the formulas of § 77, cos a — cos b cos c cos A = sin b sin c A /I +cos A /cos a — (cos b cos c — sin b sin c) = \— '-75 — =\ v . . L " 2 * 2 sin b sin ceg... | |
 | Daniel Alexander Murray - Plane trigonometry - 1899 - 350 pages
...the second member by cos A cos B cos C will give relation (2) above. 2. Show that cos (.4 + B + C) = cos A cos B cos C — cos A sin B sin C — sin A cos B sin C — sin A sin B cos C. What does this become when A + B + C = 180° ? 3. If A... | |
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A, 4 cos 6 = cos c cos a + sin c sin a cos B, > (1) . , "cos c = cos a cos b + sin a sin b cos C. J Whence . cos a — cos b... 
