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 11
... less than 90o . For instance , in the case of the angle BAC greater than 90 ° , the base AN is situated to the left of A , while before it was situated to the right . These contrarieties of position may be taken account of in 11.
... less than 90o . For instance , in the case of the angle BAC greater than 90 ° , the base AN is situated to the left of A , while before it was situated to the right . These contrarieties of position may be taken account of in 11.
Página 13
... less than 90 ° . With re- spect to the hypothenuse , it is necessary to take only its magnitude into account ; for its position is fixed by the other two sides , and can- not be determined by the signs + and since it does not remain ...
... less than 90 ° . With re- spect to the hypothenuse , it is necessary to take only its magnitude into account ; for its position is fixed by the other two sides , and can- not be determined by the signs + and since it does not remain ...
Página 19
... less than 90o . We must first suppress 360 ° as often as we can , and the sine , cosine , and tangent remain unaltered . We must next suppress 180 ° ( if the angle exceed 180 ° ) and change the signs of sine and cosine , but not of ...
... less than 90o . We must first suppress 360 ° as often as we can , and the sine , cosine , and tangent remain unaltered . We must next suppress 180 ° ( if the angle exceed 180 ° ) and change the signs of sine and cosine , but not of ...
Página 24
... less than 90 ° ; and to require that A exceed B in the formulæ relative to A - B . It is true we may modify the constructions so as to be applicable to all other cases ; but as these cases are numerous , the following mode of estab ...
... less than 90 ° ; and to require that A exceed B in the formulæ relative to A - B . It is true we may modify the constructions so as to be applicable to all other cases ; but as these cases are numerous , the following mode of estab ...
Página 29
... 90o , sin is positive and less than sin 45o , cos A - 2 2 is positive and greater than cos 45 ° ; hence the formulæ will be those at Art . 42 , with the signs which are there in evidence . If A be between 180 ° and 270 ° , sin will be ...
... 90o , sin is positive and less than sin 45o , cos A - 2 2 is positive and greater than cos 45 ° ; hence the formulæ will be those at Art . 42 , with the signs which are there in evidence . If A be between 180 ° and 270 ° , sin will be ...
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.