New Plane and Spherical Trigonometry |
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A'BC abscissa acute angle adjacent side angle corresponding BD OD BD C₁ check formula circle circular measure colog cologarithms cos a cos cos² cos²x cos³ cosecant cosine cotangent dist equal equation EXAMPLES expressed find log Find the angle find the logarithmic Find the value Geometry Given log Hence hypotenuse log cot log csc log sec log sin log tan logarithmic sine LOGARITHMS OF NUMBERS manner mantissa multiplying Note number corresponding Plane positive angle prove radius ratio result right angle right spherical triangle right triangle sec² secant significant figure sin B sin sin x cos sin² sin²x sin³ solution of oblique Solve the following Spherical Trigonometry subtract table of logarithmic tabular difference tan-¹a tan² terminal line trigonometric functions Whence by definition wwww wwwwww wwwwwwwwww ΤΟ бо ос بن بن بن
Popular passages
Page 87 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
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 62 - 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.
Page 43 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 63 - 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 81 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (g'). If A'B'C' is the polar triangle of ABC, that is, if A, -B, and С are the poles of the arcs a', b', and c', respectively, then, conversely, А B С is the polar triangle of A'B'C'.
Page 36 - ... in a direction contrary to the motion of the hands of a watch, with — and be this particularly noted — a constant tendency to turn inwards towards the centre of lowest barometer.
Page 95 - In any spherical triangle, the greater side is opposite the greater angle; and conversely, the greater angle is opposite the greater side.
Page 81 - In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. Let ABC and A'B' C' be two polar triangles. Let the sides AB and AC, produced if necessary, meet the side B'C
Page 42 - Hence, the characteristic of the logarithm of a number greater than 1 is 1 less than the number of places to the left of the decimal point. For example, the characteristic of log 906328.51 is 5.