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abscissa according acute angle Algebra angle corresponding assumes base called characteristic circle circular measure colog column computation correction corresponding cosecant cosine cotangent decimal definition denote difference distance Dividing draw equal evident EXAMPLES expressed feet figures find the angle find the logarithm find the values formulæ fourth fraction functions Geometry Given gives Hence hold included increases length less limit log csc log sin loga logarithm manner mantissa method miles minutes multiply natural negative Note observed obtain OC OC opposite ordinate perpendicular Plane positive produced proof prove putting quadrant radius ratio regard remaining Required respectively result right triangle rule secant side similar sine siny solution subtract taken tangent terminal line third tower unit unity Whence written
Side 75 - 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.
Side 92 - 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
Side 74 - 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.
Side 55 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Side 48 - ... 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.
Side 92 - ... miles an hour. How far apart are they at the end of 10i hours ? 17.