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" ... the sign of cos A, is the same as that of cos a, that is, A and a are in the same quadrant. "
A Treatise on Plane and Spherical Trigonometry - Page 179
by William Chauvenet - 1852
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...differs more from 90° than B, or than C, cos A is numerically greater than cos B, or than cos G, and the sign of cos a is the same as that of cos A, that is, a and A are in the same quadrant. For, by means of (188), tim i (a -+- b) cos % (A + 7?) = tan $ c cos £ (A — B), in which the second...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...90° than B, or than C, cos A is numerically greater than cos Д or than cos C, and the sign of сов a is the same as that of cos A, that is, a and A are in the sume quadrant. VIII. When the sum of two sides is greater títan, equal to, or ffss than 180°, the...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...or than cos c, and we have cos a > cos b cos c ; hence, the sign of the numerator, and consequently the sign of cos A, is the same as that of cos a, that is, /( and a are in the same quadrant. VII. An angle which differs more from 90° than another angle, is...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...differs more from 90° than B, or than C, cos .4 is numerically greater than cos B, or than cos 6', and the sign of cos a is the same as that of cos A, that is, a and A are in the same quadrant. BOOK V. For, by means of (188), tan £ (a -)- J) cos % (A -f B) = tan £ c cos £ (.4 — . 5), in...
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...differs more from 90° than B, or than C, cos A is numerically greater than cos B, or than cos C, and the sign of cos a is the same as that of cos A 9 that is, a and A are in the same quadrant For, by means of (188), tan £ (a -f b) cos £ (A -f- B)...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1867 - 188 pages
...or than cos c, and we have cos a > cos b cos c ; hence, the sign of the numerator, and consequently the sign of cos A, is the same as that of cos a, that...which differs more from 90° than another angle, is of the same species as its opposite side. For, by (153), we have cos A = sin B sin G cos a — cos...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...differs more from 90° than B, or than C, cos A is numerically greater than cos B, or than cos C, and the sign of cos a is the same as that of cos .1. that is, a and A are in the same quadrant. For, by means of (188), tan £ (a -j- 5) cos £ (A -\-...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...differs more from 90° than Д or than C, cos A is numerically greater than cos Д or than cos C, and the sign of cos a is the same as that of cos A, that is, a and A are in the вате quadrant. BOOK V. For, by means of (188), tan ¿ (a -\- b) cos ¿ (A -{- B) = tan ¿ с cos...
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Catalogue - Harvard University

Harvard University - 1876 - 554 pages
...may the centre be taken in this case 1 MATHEMATICS 3. 1. Prove that, in a spherical oblique triangle, an angle which differs more from 90° than another...angle is in the same quadrant as its opposite side. cos C + cos A cos B = sin A sin B cos c. 2. In the spherical oblique triangle MNO, given m, n, M; obtain,...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - Trigonometry - 1876 - 226 pages
...side which differs more from 90° than another side is in the same quadrant as its opposite angle. o. An angle which differs more from 90° than another...angle is in the same quadrant as its opposite side. § 3. The solution of all spherical triangles may be made to depend upon the solution of those each...
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