Manual of plane trigonometry, by J.A. Galbraith and S. Haughton
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Manual of Plane Trigonometry, by J.A. Galbraith and S. Haughton
Joseph Allen Galbraith
Sin vista previa disponible - 2016
Manual of Plane Trigonometry, by J. A. Galbraith and S. Haughton
Joseph Allen Galbraith
Sin vista previa disponible - 2015
Términos y frases comunes
added already Calculate the value called centre Chap characteristic circle column complement consider corres corresponding corresponding number cosecant decimal degrees and minutes derived diff divide division equal equation EXAMPLES expression feet fifth find the angle find the area Find the logarithm find the number Find the product Find the quotient find the value five figures found the mantissa four figures Given log Given the logarithm greater increase length less log cosine log sin log sine lower mantissa Multiply natural sines negative obtain proceed by RULE PROPOSITION quantities radius reason relations required to find respectively result right-angled triangle root RULE seconds sect side signifies similar sines and cosines square root Substituting subtends subtract supplement tables Tables of Natural tabular difference tangent triangle trigonometrical unity
Página 7 - For convenience, the quadrant is divided into 90 equal parts, each of which is called a degree ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are denoted by the symbols °, ', ". Thus, the expression 7° 22' 33", is read, 7 degrees, 22 minutes, and 33 seconds.
Página 12 - We have, then, that the sine of an angle is equal to the cosine of its complement, and conversely.
Página 27 - To express the cosine of the sum of two angles in terms of the sines and cosines of the angles themselves.
Página 55 - In order to apply logarithmic calculations to trigonometrical quantities, it is necessary to construct tables of the logarithms of the natural sines, cosines, &c. As all the sines and cosines, all the tangents from o° to 45°, and all the cotangents from 45° to 90°, are less than unity, the logarithms of these quantities have negative characteristics. In order to avoid the necessity of entering negative numbers, ю is added to every logarithm before it is registered in the tables of logarithmic...
Página 40 - Hence the characteristic is n — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and is positive.
Página 4 - S3". 6. Besides the above-mentioned unit of angular measure, viz. the 90th part of a right angle, which is always used in practical applications, there is another, viz. the angle at the centre of a circle which is subtended by an arc equal to the radius of the circle, which is more convenient in analytical investigations.
Página 37 - That is : The area of a triangle is equal to half the product of two sides and the sine of the included angle.
Página 50 - Ie. f"nd the logarithm of the number whose root is to be found. 2°. Divide this logarithm by the index of the given root; the quotient will be the logarithm of the required root, 3".
Página 36 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Página 37 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.