 | English literature - 1811 - 572 pages
...have Sin. A. Cos. B + Cos. A. Sin. B — t- ' and Sin.c = Sin.(180* — A + B) = Sin. A + B, since the sine of an angle is equal to the sine of its supplement. Hence Sin. A + B = Sin. A. Cos. B 4- Cos. A. Sin. BQED All this is perfectly legitimate ; but how is... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...CB : CA :: sin. A : sin. JB; CA hence sin. U = „-£ x sin. ^/, and may .'. be determined. But as the sine of an angle is equal to the sine of its supplement, the angle B may be greater or less than a right angle, unless BC be greater than AC and consequently... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...A e CB : CA :: sin. A : sin. B•, CA hence sin. B = ~ x sin. A, and may .-. be determined. But as the sine of an angle is equal to the sine of its supplement, the angle B may be greater or less than a right angle, unless BC be greater than AC and consequently... | |
 | Robert Gibson - Surveying - 1821 - 594 pages
...when the given angle is acute and opposite the lesser of the given sides, the answer is ambiguous, as the sine of an angle is equal to the .sine of its supplement, consequently the required angle opposite that other given side may be obtuse, or acute ; unless it... | |
 | Ferdinand Rudolph Hassler - Trigonometry - 1826 - 208 pages
...No. l, of the series A, or first definition, we have in the two triangles, and in both cases, (since the sine of an angle is equal to the sine of its supplement.) dd — = sin С ; and — = sin В b Therefore : d = i . sin С = с . ein B Or, expressed in a proportion... | |
 | Ferdinand Rudolph Hassler - Astronomy - 1826 - 640 pages
...No. 1, of the series A, or first definition, we have in the two triangles, and in both cases, (since the sine of an angle is equal to the sine of its supplement.) dd — = sin C ; and — = sin B bc Therefore : d = b . sin C = c . sin B Or, expressed in a proportion... | |
 | Charles Davies - Surveying - 1830 - 390 pages
...sine of the arc GF, the supplement of ABF (29), and OH is its cosine (31) ; hence, the sine of. an arc is equal to the sine of its supplement ; and the cosine of an angle, to the cosine of its supplement. Furthermore, AQ is the tangent of the arc AEF (32), and OQ is its... | |
 | Robert Gibson - Surveying - 1832 - 290 pages
...when the given angle is acute, and opposite the less of the given sides,the answer is ambiguous, as the sine of an angle is equal to the sine of its supplement, consequently the required angle opposite that other given side may be obtuse or acute, unless if is... | |
 | Henry Pearson - Algebra - 1833 - 164 pages
...an angle is equal to the sine of its complement. C 7. Sin (TT - 9) = sin 9, cos (TT - 9) = - cos Q. Or the sine of an angle is equal to the sine of its...an angle is equal to the cosine of its supplement, with its algebraical sign changed. B 8. PROPOSITION. To find expressions for the sines and cosines... | |
 | John Charles Snowball - 1837 - 322 pages
...determine B from (ii), С and с are known from (i) and (iii), and the triangle is determined. Now the sine of an angle is equal to the sine of its supplement, and therefore there are two angles which satisfy (ii), the one greater and the other less than 90°. (1).... | |
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OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an... 
