A Treatise on Plane and Spherical Trigonometry

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J.B. Lippincott & Company, 1856 - Trigonometry - 256 pages
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Page 167 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 58 - THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 149 - 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 225 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 150 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 167 - C or, when (7=90°, cos с = cos a cos 5 '(84) that is, the cosine of the hypotenuse is equal to the product of the cosines of the two sides.
Page 65 - The side opposite the given angle is to the side opposite the required angle as the sine of the given angle is to the Bine of the required angle.
Page 151 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 176 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Page 16 - The sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity.

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