 | Mathematics - 1835 - 684 pages
...А ВС sin. A cos. A = tan. A = sin. B = cos. B = tan. B = ' sin. В sin. С А В ВС (55.) То express the cosine of an angle of a triangle in terms of the sides. By Euclid, Props. 12 and 13, b. ¡¡., and Geometry, I. § 6. Prop. 37, we have AC8 = AB'+BC2-2 AB.BD... | |
 | John Charles Snowball - 1837 - 322 pages
...the angle BOC, — if it fall without it, the proposition admits of a proof in the same words. 29- To express the cosine of an angle of a, triangle in terms of the cosines und sines of the sides. From any point D in OA draw DE and DF in the planes AOB and AOC at... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...therefore in both, = . bc In like manner, sin A sin />' sin (.'. abc which proves the theorem. 30. To express the cosine of an angle of a triangle in terms of the sides. With the same figures as in the last proposition, we have in fig. 1, therefore in both cases, cos B... | |
 | Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...same length, inclined at an angle 0 to the former may properly be represented, and apply the method to express the cosine of an angle of a triangle in terms of the sides. 4. Through any point of a chord of a circle other chords are drawn ; shew that lines from the middle... | |
 | Great Britain. Committee on Education - Education - 1848 - 514 pages
...hat calculations the other parts of the triangle may be obtained. 3. Write down the expression for the cosine of an angle of a triangle in terms of the sides, and prove the expression for the sine of an angle, and for Ihe area of the triangle, in terms of the... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...as a first course in this department of mathematical science. 3. (a) " Write down the expression for the cosine of an angle of a triangle in terms of the sides and prove the expression for the sine of an angle and for the area of a triangle, in terms of the sides.... | |
 | Great Britain. Council on Education - Education - 1848 - 532 pages
...of logarithms on which the utility of logarithmic tables depends ? 3. Write down the expression for the cosine of an angle of a triangle in terms of the sides, and prove the expression for the sine of an angle, and for the area of the triangle, in terms of the... | |
 | John William Colenso (bp. of Natal.) - 1851 - 148 pages
...: c :: sinA : siuB : sin C; sinA sin-B s\nC or, as it may be also written. = — = — = . abc 106. To express the cosine of an angle of a triangle in terms of its sides. Let ABC be any triangle, and from (7, as before, draw CD perpendicular on AB, or on AB produced.... | |
 | John William Colenso (bp. of Natal.) - 1851 - 382 pages
...cosC+cosA 120. Apply the last result to shew that sin .4 :sinl? :: a : b, assuming the expression for the cosine of an angle of a triangle in terms of the sides. 121. Shew that, in any plane triangle, с = (a -6) sec0, where ф is given by the formula tanci = sin^A.... | |
 | George Wirgman Hemming - 1851 - 176 pages
...parts ; but the formulae of the next article are in certain cases more convenient in practice. 54. To express the cosine of an angle of a triangle in terms of its sides. Let A be the angle whose cosine is required. Draw CD perpendicular to AB or AB produced.... | |
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To express the cosine of an angle of a triangle in terms of the sides. Let ABC be a triangle ; and retaining the usual notation of Trigonometry, let CB = a, CA=ß; then (vector AB)' =(a- ß)' = a'-2Saß + ß 
