### Popular passages

Page 80 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 75 - 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 74 - ... 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 70 - 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 68 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 74 - CAB = 180� - A. Therefore cos a = cos b cos с + sin b sin с cos A. Hence in any spherical triangle cos a = cos b...
Page 6 - This angle is said to be in the first, second, third, or fourth quadrant according as the terminal line OP falls in one or other F1G.
Page 86 - In addition to these four cases we shall find that, when given two sides and an angle opposite one of them, or two angles and a side opposite one of them...
Page 3 - ... generally, Analytical Trigonometry. This subject is a large one, and has close connections with many other branches of modern mathematics. The system of angular measurement now to be described, is sometimes referred to as the theoretical system of measurement. In this system the unit angle is the angle which at the centre of a circle subtends an arc equal in length to the radius. This unit angle is called a radian. Thus, if a circle with any radius be described about 0 as a centre, and an arc...