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abscissa acute angle aid of Art angle AOB angle corresponding BD OD BD characteristic circle circular measure co-ordinates colog cologarithm column common logarithm cos2 cos2x cosecant cosine cosy cotangents of angles decimal point distance Dividing escM EXAMPLES find log find the angle find the logarithm find the values following triangles fourth quadrant functions of 90 Geometry Given log Hence hypotenuse included angle initial line log cos log cot log esc log sin log tan loga logarithmic sine logarithms of numbers mantissa multiply negative angle Note Number corresponding oblique triangles obtain the formulae ordinate perpendicular to OA positive angle prove the formula radius ratio right triangle rule of Art sec XOP secant second quadrant sin2 sines and cosines siny solution subtract table of natural tabular difference tan2 tangent TANGENTS AND COTANGENTS terminal line three figures trigono trigonometric functions Whence by definition Whence we obtain x sin y
Pàgina 73 - 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.
Pàgina 90 - ACB are measured, and found to be 126° 35' and 31° 48', respectively. Required the distance AB. 1. A flagpole 40 feet in height stands on the top of a tower. From a position near the base of the tower, the angles of elevation of the top and bottom of the pole are 38° 53
Pàgina 72 - 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 53 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Pàgina 46 - ... 77. By aid of the principles of Art. 76, any relation involving direct functions may be transformed into one involving inverse functions. Take for example the formula sin (x + y) = sin x cos у + cos x sin y. (A) Let sin x = a, and sin y = b. Then by Art. 76, x = sin-1 a, and у = sin-1 b.
Pàgina 90 - ... miles an hour. How far apart are they at the end of 10i hours ? 17.