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 2
... latter division is generally adopted . 5. We shall however here shew how common degrees may be converted into grades , and vice versa . Let g represent the magnitude of an angle of 15 , and d that of an angle of 1o , and let G , D , be ...
... latter division is generally adopted . 5. We shall however here shew how common degrees may be converted into grades , and vice versa . Let g represent the magnitude of an angle of 15 , and d that of an angle of 1o , and let G , D , be ...
Página 9
... latter formulæ enable us to find the values of tan 4 , sec A , & c . when those of sin A and cos A are known . Ex . 1. Suppose A = 45o . Let ABC ( fig . 5. ) be an isosceles triangle , right - angled at C ; then the other angles are ...
... latter formulæ enable us to find the values of tan 4 , sec A , & c . when those of sin A and cos A are known . Ex . 1. Suppose A = 45o . Let ABC ( fig . 5. ) be an isosceles triangle , right - angled at C ; then the other angles are ...
Página 12
... latter angle C , we have C = A + B , or C - A - B , according as AC falls above or below AB ; both of which for- mulæ may be included in a single one , C = A + B , if we affect B with a positive or negative sign , according as the angle ...
... latter angle C , we have C = A + B , or C - A - B , according as AC falls above or below AB ; both of which for- mulæ may be included in a single one , C = A + B , if we affect B with a positive or negative sign , according as the angle ...
Página 26
... latter we substitute successively 1 - sin ' A for cos A , and 1 cos3 A for sin A , we find ww cos 2 A = 1 - 2 sin2 4 , cos 2 A = 2 cos3 A - 1 , where cos 2A is expressed by sin A only , and by cos A only . 39. Next in the expressions ...
... latter we substitute successively 1 - sin ' A for cos A , and 1 cos3 A for sin A , we find ww cos 2 A = 1 - 2 sin2 4 , cos 2 A = 2 cos3 A - 1 , where cos 2A is expressed by sin A only , and by cos A only . 39. Next in the expressions ...
Página 27
... latter of the above equations , and extracting the root , we find A sin - -- = 2 cos A 2 A 1 + cos A COS = 2 2 In these expressions the radical has a double sign ; the reason why we obtain two values , equal in magnitude but of contrary ...
... latter of the above equations , and extracting the root , we find A sin - -- = 2 cos A 2 A 1 + cos A COS = 2 2 In these expressions the radical has a double sign ; the reason why we obtain two values , equal in magnitude but of contrary ...
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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.