Plane Trigonometry

Leach, Shewell, & Sanborn, 1887 - 103 sider

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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 45 - A sin B sin (A — B) = sin A cos B — cos A sin B cos (A + B) = cos A cos B...
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.
Side 56 - ... the logarithm of any power of a quantity is equal to the logarithm of the quantity multiplied by the exponent of the power. Assume the equation a

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