## New Plane and Spherical Trigonometry |

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### Common terms and phrases

1+tan A'BC abscissa acute angle adjacent side angle corresponding BD OD BD C₁ check formula circle circular measure colog cologarithms cos² cos³ cosecant cosine cotangent cubic equation dist equal equation EXAMPLES expressed find log Find the angle find the logarithmic Find the value Geometry Given log Hence hypotenuse log cot log csc log sec log sin log tan logarithmic sine LOGARITHMS OF NUMBERS manner mantissa multiplying Note number corresponding oblique spherical triangles OBLIQUE TRIANGLE positive angle prove radius ratio result right angle right spherical triangle right triangle secant significant figure sin B sin sin x cos sin² sin²x solution of oblique Solve the following SPHERICAL TRIGONOMETRY subtract table of logarithmic tabular difference tan² tanc terminal line trigonometric functions Whence by definition wwww x cos y XOP₁ ΙΟ

### Popular passages

Page 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...

Page 63 - 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 62 - 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 6 - ... in a direction contrary to the motion of the hands of a watch, with — and be this particularly noted — a constant tendency to turn inwards towards the centre of lowest barometer.

Page 44 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 97 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 43 - The logarithm of a product is equal to the sum of the logarithms of its factors.

Page 81 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 87 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 95 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.