## Elements of Plane and Spherical Trigonometry: With Numerous Examples |

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1st quadrant 3d quadrant acute angle algebraically ambiguity angle AOP angle of elevation centre circle circular measure colog cos a cos cos a sin cos² cos²x cosb cosec cosine cotangent denote equal equation EXAMPLES express feet high find the height Find the number formulæ formulæ of Art Geometry Given two sides greater than 90 Hence hypotenuse included angle Introduction price length Let ABC log cot logarithms Napier's Rules negative observed opposite angle perpendicular plane polar triangle positive Prove the following quadrant quadrantal triangle radian radius respectively revolving line right angles right triangle secant Sexagesimal Similarly sin A cos sin b sin sin² sin2b sin²x sinx siny solution of triangles spherical triangle SPHERICAL TRIGONOMETRY subtends tan-¹ tan² tan²x tangent tany three angles tions trigonometric functions yards

### Popular passages

Page 71 - 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 70 - Law of Sines - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...

Page 121 - 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 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...

Page 72 - 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 119 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...

Page 115 - Rules are : (1) The sine of the middle part equals the product of the tangents of the adjacent parts. (2) The sine of the middle part equals the product of the cosines of the opposite parts.

Page 121 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.

Page 109 - On the bank of a river there is a column 200 feet high, supporting a statue 30 feet high ; the statue to an observer on the opposite bank subtends the same angle as a man 6 feet high standing at the base of the column : find the breadth of the river.

Page 3 - O in the direction contrary to that of the hands of a watch.