## Plane Trigonometry |

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Plane Trigonometry Henry Wadsworth Longfellow,Webster Wells,Samuel Longfellow No preview available - 2016 |

### Common terms and phrases

abscissa according acute angle Algebra angle corresponding assumes base calculated called characteristic circle circular measure colog column correction cos x cos² cosecant cosine cotangent decimal definition denote difference distance Dividing draw equal evident EXAMPLES expressed feet figures Find the angles find the logarithm find the values formulæ fourth functions Geometry Given gives Hence included increases length less limit log csc log sin logarithm manner mantissa method miles minutes multiply negative Note observed obtain opposite ordinate perpendicular Plane positive produced prove putting quadrant radius ratio remaining Required respectively result right triangle rule secant side similar sin A sin sin² sine sines and cosines solution subtract taken tangent terminal line third unit Whence written

### Popular passages

Page 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.

Page 45 - A sin B sin (A — B) = sin A cos B — cos A sin B cos (A + B) = cos A cos B...

Page 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

Page 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.

Page 55 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 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.

Page 92 - ... miles an hour. How far apart are they at the end of 10i hours ? 17.

Page 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