| Mathematics - 1835 - 684 pages
...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
...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
...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
...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
...side, show by w 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
...great utility 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
...the properties 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 - 382 pages
...- . smB cosB 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
...53. The sides of a triangle are proportional to the sines of the opposite angles 84 54. To express the cosine of an angle of a triangle in terms of the sides 85 56. On the solution of right-angled triangles . . 88 57. On the solution of oblique-angled triangles... | |
| Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...= sin. arc cb. One of the most important formulae in spherical trigonometry is that which expresses the cosine of an angle of a triangle, in terms of the three sides. To obtain this formula we may employ fig. 115, where abc is a spherical triangle, o the... | |
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