Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 4
... derived the number which represents a right angle . The arc which sub- tends a right angle is equal to a fourth part of the circumference , or πr , by equation ( 2 ) . Dividing this by r we obtain , by equation ( 1 ) , The numerical ...
... derived the number which represents a right angle . The arc which sub- tends a right angle is equal to a fourth part of the circumference , or πr , by equation ( 2 ) . Dividing this by r we obtain , by equation ( 1 ) , The numerical ...
Página 7
... derived from geometrical principles as follows . Because the triangles BCP , ACT , and CDS are right - angled , it follows ( Euclid , Book I. Prop . XLVII . ) that = CB2 = BP2 + CP2 , CT2 = CA2 + AT2 , CS2 = CD2 + DS2 . As the radius of ...
... derived from geometrical principles as follows . Because the triangles BCP , ACT , and CDS are right - angled , it follows ( Euclid , Book I. Prop . XLVII . ) that = CB2 = BP2 + CP2 , CT2 = CA2 + AT2 , CS2 = CD2 + DS2 . As the radius of ...
Página 27
... derived a great variety of useful formula : sin ( A + B ) = sin A cos B + cos A sin B , cos ( A + B ) = cos A cos B- sin A sin B , sin ( A – B ) = sin A cos B- cos A sin B , cos ( A - B ) = cos A cos B + sin A sin B. By adding equations ...
... derived a great variety of useful formula : sin ( A + B ) = sin A cos B + cos A sin B , cos ( A + B ) = cos A cos B- sin A sin B , sin ( A – B ) = sin A cos B- cos A sin B , cos ( A - B ) = cos A cos B + sin A sin B. By adding equations ...
Página 29
... derived from them is perfectly general , i . e . true for all values of A ' and B , and therefore for A and B. It is for this reason that we are at liberty to remove the accents after transformation . or If in equation ( 1 ) we suppose ...
... derived from them is perfectly general , i . e . true for all values of A ' and B , and therefore for A and B. It is for this reason that we are at liberty to remove the accents after transformation . or If in equation ( 1 ) we suppose ...
Página 33
... derived from the expression , which gives the value of the cosine of any angle in terms of the sides . This expression may be deduced as follows : in fig . 12 let the angle A be acute , we have ( Euclid , Book . II . Prop . XIII . ) but ...
... derived from the expression , which gives the value of the cosine of any angle in terms of the sides . This expression may be deduced as follows : in fig . 12 let the angle A be acute , we have ( Euclid , Book . II . Prop . XIII . ) but ...
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
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...