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 52
... nearly ( Art . 28 , App . ) ......... ( 5 ) .. logƒ ( 0 ± k ) = log ƒ ( 0 ) + μ Pk ́ƒ ( 0 ) * But log f ( 0k ) -logƒ ( 0 ) is the difference given in the tables , - 8 suppose , so that μP 8 ' ƒ ( 0 ) ̄ k ・= Hence , substituting in ( 5 ) ...
... nearly ( Art . 28 , App . ) ......... ( 5 ) .. logƒ ( 0 ± k ) = log ƒ ( 0 ) + μ Pk ́ƒ ( 0 ) * But log f ( 0k ) -logƒ ( 0 ) is the difference given in the tables , - 8 suppose , so that μP 8 ' ƒ ( 0 ) ̄ k ・= Hence , substituting in ( 5 ) ...
Página 53
... nearly a right angle , its value , and consequently the value of log - sin ( 0+ h ) -log - sin 0 , is exceedingly small ; and similarly the expression for cos ( 0 - h ) - cos shews that its value , as well as that of log - cos ( 0 - h ) ...
... nearly a right angle , its value , and consequently the value of log - sin ( 0+ h ) -log - sin 0 , is exceedingly small ; and similarly the expression for cos ( 0 - h ) - cos shews that its value , as well as that of log - cos ( 0 - h ) ...
Página 54
... nearly equal . diff . 377886 , diff . 413927 , Hence , when an angle A is to be determined from an equation of the form tan A = a , where a is considerable , so that A is nearly 90o , we must replace it by the formula tan ( 4-45o ) ...
... nearly equal . diff . 377886 , diff . 413927 , Hence , when an angle A is to be determined from an equation of the form tan A = a , where a is considerable , so that A is nearly 90o , we must replace it by the formula tan ( 4-45o ) ...
Página 60
... nearly a right angle , and is to be determined by a formula which for that particular value of the angle is incompetent to furnish great numerical accuracy , the formula must be transformed into an- other free from that defect , in the ...
... nearly a right angle , and is to be determined by a formula which for that particular value of the angle is incompetent to furnish great numerical accuracy , the formula must be transformed into an- other free from that defect , in the ...
Página 66
... nearly 90 ° , we must avoid determining it by its sine or tangent , and when it is very small , we must avoid determining it by its cosine ; and that when 4 is less than 45 ° , the tables will determine it from its sine with greater ...
... nearly 90 ° , we must avoid determining it by its sine or tangent , and when it is very small , we must avoid determining it by its cosine ; and that when 4 is less than 45 ° , the tables will determine it from its sine with greater ...
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.