Plane and Spherical Trigonometry

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Silver, Burdett & Company, 1894 - 206 pàgines
 

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Pàgina 147 - 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...
Pàgina 57 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Pàgina 144 - 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...
Pàgina 142 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Pàgina 149 - С . cos A = — cos B . cos С + sin B . sin С . cos « . III. cos B = — cos A . cos С + sin A . sin С . cos ß . cos G = — cos A . cos B...
Pàgina 129 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Pàgina 49 - ... base is to the sum of the other two sides, as the difference of those sides is to the difference of the segments of the base.
Pàgina 158 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Pàgina 100 - ... b) = sec b, cosec ( — b) = — cosec b ; (53) that is, the cosine and secant of the negative of an angle are the same as those of the angle itself ; and the sine, tangent, cotangent, and cosecant of the negative of an angle are the negatives of those of the angle. These results correspond with those obtained geometrically (Art. 68). 80.

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