Manual of plane trigonometry, by J.A. Galbraith and S. Haughton

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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.

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