Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 17
... corresponds in the tables to 8 ° ; the complement of this 82 ° = B. If the squares of a and b be added , the sum is 254937.8729 ; the square root of this being taken , we find 504.91 . 2. Given α = 141.407 , and b = 3. Given a = Ans . c ...
... corresponds in the tables to 8 ° ; the complement of this 82 ° = B. If the squares of a and b be added , the sum is 254937.8729 ; the square root of this being taken , we find 504.91 . 2. Given α = 141.407 , and b = 3. Given a = Ans . c ...
Página 20
... corresponding angle : log tan A = 10.3925893 log tan 67 ° 57 ′ = 10.3925003 Tab . diff . 3631 , = 890 = diff . 890 × 60 = 3631 Ans . 14 " . - A = 67 ° 57 ′ 14 ′′ . B 22 ° 2 ′ 46 ′′ . = To find c , 10+ log 121 = 12.0827854 log 20 RIGHT ...
... corresponding angle : log tan A = 10.3925893 log tan 67 ° 57 ′ = 10.3925003 Tab . diff . 3631 , = 890 = diff . 890 × 60 = 3631 Ans . 14 " . - A = 67 ° 57 ′ 14 ′′ . B 22 ° 2 ′ 46 ′′ . = To find c , 10+ log 121 = 12.0827854 log 20 RIGHT ...
Página 36
... corresponds with the result otherwise obtained in Prop . I. If for the value of 1 + cos A obtained in equation ( 2 ) we substitute its equal , 2 cos2A ( Chap . IV . ( 23 ) ) ; and for the factors ( a + b + c ) and ( b + c − a ) their ...
... corresponds with the result otherwise obtained in Prop . I. If for the value of 1 + cos A obtained in equation ( 2 ) we substitute its equal , 2 cos2A ( Chap . IV . ( 23 ) ) ; and for the factors ( a + b + c ) and ( b + c − a ) their ...
Página 37
... sin Bin C. This corresponds with the result otherwise obtained in Prop . I. If for the value ( 3 ) we substi ( 83 ) ) ; and their val 71 3 S RELATION BETWEEN THE Taking the square root. 36 RELATION BETWEEN THE SIDES AND ANGLES ,
... sin Bin C. This corresponds with the result otherwise obtained in Prop . I. If for the value ( 3 ) we substi ( 83 ) ) ; and their val 71 3 S RELATION BETWEEN THE Taking the square root. 36 RELATION BETWEEN THE SIDES AND ANGLES ,
Página 37
... corresponds with the result otherwise obtained in Prop . I. If for the value of 1 + cos A obtained in equation . ( 2 ) we substitute its equal , 2 cos2A ( Chap . IV . ( 23 ) ) ; and for the factors ( a + b + c ) and ( b + c - a ) their ...
... corresponds with the result otherwise obtained in Prop . I. If for the value of 1 + cos A obtained in equation . ( 2 ) we substitute its equal , 2 cos2A ( Chap . IV . ( 23 ) ) ; and for the factors ( a + b + c ) and ( b + c - a ) their ...
Otras ediciones - Ver todas
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
Pasajes populares
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.