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 10
... obtained , not through the sine , but directly from the figure ; for AD = 1AB , and DB2 = AB2 – AD2 = { AB3 , or DB = √3 . AB ; ᎠᏴ AD .. cos 30 ° = AB = √3 , tan 30 ° = = DB √3 = 3√3 , & c . 18. The five formulæ of Art . 16 are ...
... obtained , not through the sine , but directly from the figure ; for AD = 1AB , and DB2 = AB2 – AD2 = { AB3 , or DB = √3 . AB ; ᎠᏴ AD .. cos 30 ° = AB = √3 , tan 30 ° = = DB √3 = 3√3 , & c . 18. The five formulæ of Art . 16 are ...
Página 20
... obtained for the other Trigonometrical Ratios . On the angles which correspond to given values of the sine , cosine , & c . 31. The preceding results give occasion for the important remark that there exists an infinite number of angles ...
... obtained for the other Trigonometrical Ratios . On the angles which correspond to given values of the sine , cosine , & c . 31. The preceding results give occasion for the important remark that there exists an infinite number of angles ...
Página 27
... obtain two values , equal in magnitude but of contrary signs , for each of the unknown quantities sin A , cos è̟A , is that since we are at liberty to write 2na for A under the radical , ( that being the general value of angles which ...
... obtain two values , equal in magnitude but of contrary signs , for each of the unknown quantities sin A , cos è̟A , is that since we are at liberty to write 2na for A under the radical , ( that being the general value of angles which ...
Página 33
... obtain formulæ worthy of notice as expressing the sines and cosines of multiples of an angle in terms of the sines and co- sines of inferior multiples of the same angle . From the first and third we thus deduce sin n B = 2 sin ( n − 1 ) ...
... obtain formulæ worthy of notice as expressing the sines and cosines of multiples of an angle in terms of the sines and co- sines of inferior multiples of the same angle . From the first and third we thus deduce sin n B = 2 sin ( n − 1 ) ...
Página 40
... obtained by diminishing the difference of the sines of the preceding angles n 10 ′′ and ( n − 1 ) 10 ′′ , which is already calculated , by k sin n 10 " ; so that for each new sine , the only laborious operation will be to multiply the ...
... obtained by diminishing the difference of the sines of the preceding angles n 10 ′′ and ( n − 1 ) 10 ′′ , which is already calculated , by k sin n 10 " ; so that for each new sine , the only laborious operation will be to multiply the ...
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.