## Elements of Trigonometry with Logarithmic and Other Tables |

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### Common terms and phrases

a. c. log Angle Changes angle increases angle is greater angle is passing angles which correspond centre changes its sign chord column common logarithms computed Construct both positive construction and measurement cosec cosine cotangent covers coversine denoting any angle determined distance changes distance decreases equations Examples face-angle final side following angles formulas given angle giving greater than 3600 hence the cosecant horizontal increases from 00 initial side intersects inverse function least rapidly less than 3600 log cot log tan mantissa metres minus multiplied Negative Angles oblique dihedral opposite passing through 900 perpen perpendicular positive angles less quadrant radians radius rapidly when passing reduce Requ1rtd required angle right angle right dihedral right line right triangle secant sine solution solve the trihedral spherical triangle sponding straight line supplementary angles tangent line trigonometric functions unity versed-sine versine vertex

### Popular passages

Page 98 - From the top of a cliff 150 ft. high the angles of depression of the top and bottom of a tower are 30° and 60°, respectively.

Page 100 - The sum of any two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 95 - The length of the projection of a limited line upon a plane, is equal to the length of the line multiplied by the cosine of the acute angle which it forms with the plane.

Page 63 - ... to the tangent of half their difference. Let AB, AC be two arcs of a circle ABCD ; let E be the centre, and AEG the diameter which passes through A ; sin. AC+sin. AB : sin. AC —sin. AB : : tan.

Page 96 - An angle of elevation, is a vertical angle having one of its sides horizontal, and the inclined side above the horizontal side.

Page 158 - sin В sin C' sin С sin A cos a = cos b cos с + sin 6 sin с cos A, with similar formulae for cos b and cos c. cos A = — cos В cos С + sin В sin С cos a, with similar formulae for cos В and cos C.

Page 108 - CASE II. Given two sides and an angle opposite one of them, to find the remaining parts.

Page 156 - They may cut each other, having two points common, when the distance between the centers is less than the sum and greater than the difference of the radii.