This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1868 Excerpt: ...the distance MO or PN will be denoted by a positive number when P is to the right of CC and by a negative number when P is to the left of CC. 146. Ratios. General definitions of the Trigonometrical We can now give general definitions of the Trigonometrical Ratios which will apply to angles of any magnitude. Let AB, AC ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1868 Excerpt: ...the distance MO or PN will be denoted by a positive number when P is to the right of CC and by a negative number when P is to the left of CC. 146. Ratios. General definitions of the Trigonometrical We can now give general definitions of the Trigonometrical Ratios which will apply to angles of any magnitude. Let AB, AC be two straight lines at right angles; let a straight line turn round the point A from AB towards AC and come into any position AP; draw PM perpendicular to AB or to AB produced through A. Then consider AP as always positive; consider AM as positive or negative according as M is on the same side of A C as B is, or on the opposite side; and consider PM as positive or negative according as P is on the same side of AB as C is, or on the opposite side. Let the angle PAB be denoted by A; then the Trigonometrical Ratios of A are thus defined: 147. We have therefore Trigonometrical Ratios for any positive angle whatever may be its magnitude; and we nave also Trigonometrical Ratios for any negative angle by adopting the convention that the Trigonometrical Ratios for any negative angle shall be the same as they would be for what we may call the corresponding positive angle. Thus, for example, in the last figure we may consider BAP as a negative angle, the magnitude of which is--60; then the Trigonometrical Ratios will be the same as for the angle formed by turning the moveable line AP in the positive direction until it reaches the position which it has in the figure; so that the Trigonometrical Ratios for the angle-60 will be the same as for the angle 360-60. 148. It follows immediately from the definitions that if two angles differ by four right angles or by any multiple of four right angles, the Trigonometrical Ratios of the two angles are the same. ...
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
