 | 1894 - 576 pągines
...C, these three points lie on a straight line, because the ordinary formula for a spherical triangle cos c= cos a cos b + sin a sin b cos C is easily transformed to cos a— b _ cosa + b — cose ~r-(-i) i-(-cdsC) ' So that if a square be... | |
 | Great Britain. Education Department. Department of Science and Art - 1894 - 894 pągines
...that OA', OB', OC' bisect the angles of the polar triangle A'B'C'. (35.) 29. EStablish the formula cos c = cos a cos b + sin a sin b . cos C for any spherical triangle ABC. Show that — _ /I _ : V 1 + sin r, _ /I _ cos n cos // cos i• sin... | |
 | Alexander Macfarlane - 1894 - 60 pągines
...When A, B, C, are used to denote the external angles between the sides, the above equation is written cos C = — cos A cos B — sin A sin B cos c. Apply the same rule of change to the Sine part, and we obtain Sin (TT— £17) = — cos(ir— ££)... | |
 | Frederick Anderegg, Edward Drake Roe - 1896 - 134 pągines
...— b As a check use § 79. If the side c alone is desired, it may be found from the formula, § 77, cos c = cos a cos b + sin a sin b cos C, which may be adapted to logarithmic computation by the aid of an auxiliary angle, as follows : cos... | |
 | John Bascombe Lock - 1896 - 244 pągines
...angle. cos a = cos b cos c + sin b sin c cos 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 cos c cos A = ; ; , sin b sin c cos b — cos c cos a cosB = cos С —... | |
 | George Albert Wentworth - 1899 - 392 pągines
...cos С' + sin Ь" sin С' cos a'; and similarly, cos B' = — cos A' cos С' + sin A' sin С' cos6'; cos C' = — cos A' cos B' + sin A' sin B' cos c'. EXERCISE XXXV. PAGE 157. 1. Write formulas for finding, by Napier's Rules, the side a when b, c, and... | |
 | Robert Stawell Ball - 1900 - 584 pągines
...sin a sin b sin c ' cos a = cos b cos c + sin b sin c cos A, cos b = cos c cos a + sin c sin a cos B, cos c = cos a cos b + sin a sin b cos C. Thus the formulae of spherical trigonometry are generally applicable throughout the extent*. * I learned... | |
 | Hendrik Antoon Lorentz - 1900 - 516 pągines
...man cos A = — cos B cos C + sin B sin C cos al cos B— — cos C cos A + sin C sin A cos b \ (22) cos C = — cos A cos B + sin A sin B cos c . \ § 41. Aus den Formeln (20) ergeben sich unmittelbar die Werte der Winkel, wenn die der Seiten... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - 1900 - 184 pągines
...triangles, cos a' = cos V cos c' + sin b' sin c' cos A', cos 6' = cos c' cos a' + sin c' sin a' cos .B', cos c' = cos a' cos b' + sin a' sin b' cos C". But a' — TT — -4, J.' = 77- — a, etc. Substituting these values and noting that sin (TT — x)... | |
 | Elmer Adelbert Lyman, Edwin Charles Goddard - 1900 - 228 pągines
...= — cos B cos C + sin B sin C cos a, Similarly, cos B = — cos A cos C + sin A sin C cos b, and cos C = - cos A cos B + sin A sin B cos c. 97. In any spherical triangle to prove gHLJ:=gHLg=sm C. sin a sin b sin a c • . cos a — cos 6 cos... | |
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B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G. 
