## Plane [and Spherical] Trigonometry for Colleges and Secondary Schools |

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### Common terms and phrases

acute angles algebraic appear approximately base calculated called centre changes CHAPTER circle Compare computation construction cosec cosine deduced definitions denoted derived described difference direction distance draw drawn elements equal equation EXAMPLES exercises expressed figure Find formulas geometry give given greater height Hence hypotenuse inch included increases indicated inscribed intersection known length less logarithms means measure method namely negative Note observed obtained opposite perpendicular places plane polar pole polygon positive practical problems Prove quadrant quantity radius relations represent respectively right angles right-angled triangle scale Show shown sides sine solution Solve sphere spherical triangle student subtended surface tables taken taking tangent third tions tower trigonometric functions trigonometric ratios unit

### Popular passages

Page 35 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...

Page 25 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 87 - 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 85 - 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 55 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...

Page 111 - The ratio of a circumference of a circle to its diameter is the same for all circles. [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance, to Euclid VI., 33.* The proof of (6) is not contained in all geometries ; for instance, Euclid does not give...

Page 183 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.

Page 41 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area, F THE RIGHT TRIANGLE.