Elements of Plane and Spherical Trigonometry

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J.B. Lippincott, 1890 - Trigonometry - 159 pages
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Page 66 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 93 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 98 - A. {cos a = cos b cos c + sin b sin c cos A. cos b = cos a cos c + sin a sin c cos B.
Page 95 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Page 66 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 53 - Div1ding each term of the fraction by cos x cos y, sin x cos у . cos x sin у cos x...
Page 3 - ... with clearness that portion of the subject of Trigonometry which is generally given in a college course. The first part of the subject is presented in much detail, each point being emphasized as far as possible by means of numerous examples and illustrations.
Page 136 - THEOREM. The area, of a spherical triangle is equal to its spherical excess multiplied by a tri.rectangular triangle.
Page 18 - The cosine of an angle is the ratio of the adjacent side to the...

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