Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 20
... Given a and b , it is required to find A , B , and c . By equation ( 3 ) , α tan A = 2 . b Taking the logarithm of each side , log tan A - 10 = log a log tan A = 10 + log a - - log b , log b . To find c , we have by equation ( 1 ) , C ...
... Given a and b , it is required to find A , B , and c . By equation ( 3 ) , α tan A = 2 . b Taking the logarithm of each side , log tan A - 10 = log a log tan A = 10 + log a - - log b , log b . To find c , we have by equation ( 1 ) , C ...
Página 21
Joseph Allen Galbraith. To find c , 10+ log 121 = 12.0827854 log sin 67 ° 57 ′ = 9.9670125 Tab . diff . = 512 . 512 X 14 60 = 2.1157729 119 ( Rule XI . ) By applying Rule IV . we find , log ... Given a = one mile , and b = 3 furlongs , 7 ...
Joseph Allen Galbraith. To find c , 10+ log 121 = 12.0827854 log sin 67 ° 57 ′ = 9.9670125 Tab . diff . = 512 . 512 X 14 60 = 2.1157729 119 ( Rule XI . ) By applying Rule IV . we find , log ... Given a = one mile , and b = 3 furlongs , 7 ...
Página 22
... logarithms of both sides , 2 log b = log ( c + a ) + log ( c − a ) . EXAMPLES . 1. Given a = 13.2 , and c = 127 ; find b , A , and B. 10+ log 13.2 = 11.1205739 log 127 = 2.1038037 Tab . diff . 12104 . log sin A log 5 ° 57 ...
... logarithms of both sides , 2 log b = log ( c + a ) + log ( c − a ) . EXAMPLES . 1. Given a = 13.2 , and c = 127 ; find b , A , and B. 10+ log 13.2 = 11.1205739 log 127 = 2.1038037 Tab . diff . 12104 . log sin A log 5 ° 57 ...
Página 23
... Given a = 21.7 , and c = 54.31 ; find A , B , and b . CASE III . 53 " . Ans . A 23 ° 33 ′ 2 ′′ . B = 66 ° 26 ′ 58 ′′ . b = 49.78640 . Given a and A , it is required to find B , b , and c . By equation ( 1 ) , a = c sin A ; log c = 10 + log ...
... Given a = 21.7 , and c = 54.31 ; find A , B , and b . CASE III . 53 " . Ans . A 23 ° 33 ′ 2 ′′ . B = 66 ° 26 ′ 58 ′′ . b = 49.78640 . Given a and A , it is required to find B , b , and c . By equation ( 1 ) , a = c sin A ; log c = 10 + log ...
Página 38
... given , Area cp . = By Prop . 1. Chap . III . , p = b sin A , therefore Areabc sin A. ( 9 ) From this follows ... logarithmic tables , from the equation which is derived from ( 9 ) , as follows : 2 Area = bc sin A , log ( 2 38 EXPRESSION FOR ...
... given , Area cp . = By Prop . 1. Chap . III . , p = b sin A , therefore Areabc sin A. ( 9 ) From this follows ... logarithmic tables , from the equation which is derived from ( 9 ) , as follows : 2 Area = bc sin A , log ( 2 38 EXPRESSION FOR ...
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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
a² 2bc angle ACB angle is equal angular unit appears from Prop Calculate the value centre Chap circle Circumference complement corresponding number cosec degrees and minutes diameter diff divide equation Euclid Express feet find the angle find the area Find the logarithm find the number Find the product Find the quotient find the value five figures following proportion four figures given angle Given log given side Given the logarithm hypotenuse log cosine log cotangent log sine log tangent Logarithmic Tables mantissa Natural Sines number is equal number of seconds obtain proceed by RULE PROPOSITION rence required to find right angle right-angled triangle secant sect sin A sin sines and cosines square root subtends subtract Tables of Natural tables the corresponding tabular difference triangle BCP TRIGONOMETRICAL MAGNITUDES value of log versin
Pasajes populares
Página ii - RULE. The characteristic of the logarithm of a number greater than unity, is one less than the number of integral figures in the given number.
Página iv - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 5 - ... to be divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters ° ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10° 18
Página 10 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.
Página iv - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página ii - The Characteristic of the logarithm of a number less than unity, and reduced to the decimal form, is negative and one greater than the number of cyphers following the decimal point.
Página xi - ... will be the logarithm of the quotient. 3°. Find from the Tables the corresponding number. This will be the required quotient.
Página 2 - 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 10 - We have, then, that the sine of an angle is equal to the cosine of its complement, and conversely.
Página 29 - Thus: sin (a + a) = sin a cos a + cos a sin a or: sin 2a = 2 sin a cos a...