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

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2d quadrant acute angle algebraically ambiguity angle AOP angle of elevation centesimal centre circle circular measure colog cos a cos cos0 cos2 cosB cosC cose cosec cosine cosx cosy cot2 cotangent denote equal equation EXAMPLES express feet high find the height Find the number Geometry Given find Given the three Given two sides greater than 90 Hence hypotenuse included angle Introduction price length Let ABC log cot logarithms miles Napier's Rules negative observed opposite angle perpendicular polar triangle positive Prove the following quadrantal triangle radians radius reflex angle respectively revolving line right angles right triangle secant Sexagesimal Similarly sin a cos sin A sin sin x sin(s sin0 sin2 sin2a sin2B sin2c sinB sinx siny Solve spherical triangle Spherical Trigonometry subtends tan0 tan2 tana tangent three angles three sides tions trigonometric functions yards zero

### Popular passages

Page 73 - 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 72 - Law of Sines - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...

Page 123 - 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 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 121 - 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 117 - 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 123 - ... 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 111 - 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.