A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms: Together with a Selection of Problems and Their SolutionsJ. & J.J. Deighton, and T. Stevenson, 1841 - 151 páginas |
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Página 8
... former in N , and join CN , PN ; then PCN is an angle whose sine equals a ; for on account of the right angle PNC , PN CP sin PCN = = a . If it is the cosine which is given , the construction will be the same , except that the second ...
... former in N , and join CN , PN ; then PCN is an angle whose sine equals a ; for on account of the right angle PNC , PN CP sin PCN = = a . If it is the cosine which is given , the construction will be the same , except that the second ...
Página 11
... former , we easily find cos A = ± 1 √1 + tan * A and then sin A = ± tan A √1 + tan * A the double sign implying that there exist two sines and two cosines , equal in magnitude but contrary in algebraical sign , corresponding to the ...
... former , we easily find cos A = ± 1 √1 + tan * A and then sin A = ± tan A √1 + tan * A the double sign implying that there exist two sines and two cosines , equal in magnitude but contrary in algebraical sign , corresponding to the ...
Página 16
... former one ; and the various positions of AC relative to the primitive line will be equally well determined by them as by positive angles . Thus the positions of AC ,, AC3 , may be determined by the negative angles BAC ,, BAC ,, that is ...
... former one ; and the various positions of AC relative to the primitive line will be equally well determined by them as by positive angles . Thus the positions of AC ,, AC3 , may be determined by the negative angles BAC ,, BAC ,, that is ...
Página 26
... former we substitute successively 1 - sin3 : for cos 4 , and 1 - cos for sin A , we get sin 24 = 2 sin A√1 – sin2 A , sin 2 A = 2 cos A√1 - cos2 A , where sin 2 A is expressed by sin A only , and by cos A only ; and in each case has ...
... former we substitute successively 1 - sin3 : for cos 4 , and 1 - cos for sin A , we get sin 24 = 2 sin A√1 – sin2 A , sin 2 A = 2 cos A√1 - cos2 A , where sin 2 A is expressed by sin A only , and by cos A only ; and in each case has ...
Página 27
... former members of the equations ; and therefore the above formulæ must give all values comprised in sin COS ( T2 ) , n being any integer whatever . Now , by Art . 29 , if n is even , these are the same as sin ( + ) - sin , cos ( + ) ...
... former members of the equations ; and therefore the above formulæ must give all values comprised in sin COS ( T2 ) , n being any integer whatever . Now , by Art . 29 , if n is even , these are the same as sin ( + ) - sin , cos ( + ) ...
Outras edições - Ver tudo
A treatise on trigonometry and on trigonometric tables and logarithms John Hymers Visualização integral - 1812 |
Treatise on Trigonometry and Trigonometrical Tables and Logarithms; Together ... John Hymers Pré-visualização indisponível - 2012 |
Palavras e frases frequentes
ABC fig acute angle BAC arcs bisected calculation circular measure circumscribed circle consequently cos² cos³ cosec cotangent decimal point denoted determined diff difference digits distance equal equation expressed find the angle formula given angle Hence horizontal hypothenuse included angle inscribed integer intersect less than 90 log-cos log-cosine log-sin log-tan loga logarithms magnitude multiple negative opposite angles perpendicular pole polygon positive produced quadrant quantities radius regular polygon right angle right-angled triangle sec² shew side opposite Similarly sin a sin sin² sin³ sines and cosines solid angle solution sphere spherical triangle Spherical Trigonometry subsidiary angle subtends subtracting suppose tables tan² tan³ tangent telescope three sides triangle ABC Trigono Trigonometrical Ratios values Vernier zero
Passagens conhecidas
Página 3 - ... 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.
Página 95 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 127 - suffice to afford such an approximation to it as shall be of use in the ' present stage of the reader's knowledge, and help him to many just ' conceptions, on which account we shall exemplify its application in ' numbers. Now, it appears by observation, that two points, each ten...
Página 50 - 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.
Página 49 - ... these elements must be given, one of which must be a side, in order to solve a plane triangle. The solution of plane triangles depends upon the following FUNDAMENTAL PROPOSITIONS. 109. In a right-angled triangle, the side opposite to an acute angle is equal to the product of the hypothenuse into the sine of the angle ; and the side adjacent to an acute angle is equal to the product of the hypothenuse into the cosine of the angle. Let...
Página 25 - В; by means of which we can express the sine and cosine of the sum or difference of two angles in terms of the sines and cosines of the angles themselves.
Página 17 - OP — sin A cos B + cos A sin B. OM_OQ-QM_OQ NR '" OP~ OP ~ OP OP _ OQ_ ON_NR NP "ON'OP~WP'"OP =^cos A cos .B- sin .4 sin B. 77. To express the sine and cosine of the difference of two angles in terms of the sines and cosines of the angles themselves.