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 1
... means of some of its parts ; but these constructions , on ac- count of the imperfection of the instruments employed , give only a rough and often insufficient approximation . Mathema- ticians have therefore sought to substitute for them ...
... means of some of its parts ; but these constructions , on ac- count of the imperfection of the instruments employed , give only a rough and often insufficient approximation . Mathema- ticians have therefore sought to substitute for them ...
Página 5
... means of their geometrical properties , we soon become aware of the difficulties of introducing the measures of the angles into calculation ; and we are led to re- place them by certain ratios depending upon the angles , so that they ...
... means of their geometrical properties , we soon become aware of the difficulties of introducing the measures of the angles into calculation ; and we are led to re- place them by certain ratios depending upon the angles , so that they ...
Página 8
... means of its sine , and vice versâ ; and to express the other Trigonometri- cal Ratios of an angle by means of its sine and cosine , From the right - angled triangle APN ( fig . 8 16-19 Relations of the Trigonometrical Ratios to one ...
... means of its sine , and vice versâ ; and to express the other Trigonometri- cal Ratios of an angle by means of its sine and cosine , From the right - angled triangle APN ( fig . 8 16-19 Relations of the Trigonometrical Ratios to one ...
Página 11
... means of its tangent , we must take the equations ( 1 ) and ( 2 ) , viz . sin A sin2 A + cos A = 1 , . _tan A = cos A the second gives sin A = tan A cos A , or sin2 A = tan3 A cos ' A and substituting this value of sin ' A in the former ...
... means of its tangent , we must take the equations ( 1 ) and ( 2 ) , viz . sin A sin2 A + cos A = 1 , . _tan A = cos A the second gives sin A = tan A cos A , or sin2 A = tan3 A cos ' A and substituting this value of sin ' A in the former ...
Página 15
... means of their measures , leads to the consideration of angles not only greater than two right angles , but of all possible magnitudes . With centre A ( fig . 11. ) and any radius AB describe a circle ; and suppose the radius AC ...
... means of their measures , leads to the consideration of angles not only greater than two right angles , but of all possible magnitudes . With centre A ( fig . 11. ) and any radius AB describe a circle ; and suppose the radius AC ...
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.