Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 7
Joseph Allen Galbraith. Let the right lines ( fig . 2 ) AA ' and DD ' , be drawn intersecting at right angles in the ... triangles BCP , ACT , and CDS are right - angled , it follows ( Euclid , Book I. Prop . XLVII . ) that = CB2 = BP2 + ...
Joseph Allen Galbraith. Let the right lines ( fig . 2 ) AA ' and DD ' , be drawn intersecting at right angles in the ... triangles BCP , ACT , and CDS are right - angled , it follows ( Euclid , Book I. Prop . XLVII . ) that = CB2 = BP2 + ...
Página 10
... angle , and ACB ' ( fig . 3 ) its sup- plement , then as B'CA ' is the supplement of ACB ' , it is equal to ACB ; from which it follows ( Euclid , Book I. Prop . XXVI . ) that the right - angled triangles BPC and B'P'C are equal in ...
... angle , and ACB ' ( fig . 3 ) its sup- plement , then as B'CA ' is the supplement of ACB ' , it is equal to ACB ; from which it follows ( Euclid , Book I. Prop . XXVI . ) that the right - angled triangles BPC and B'P'C are equal in ...
Página 12
... angle 45 ° , which is equal to half a right angle ; by equation ( 1 ) , I = sin2 45 ° + cos2 45 ° . Ι But as the triangle BCP is in this case ( fig . 5 ) a right - angled isosceles triangle , it is evident that sin 45 ° cos 45 ° , and ...
... angle 45 ° , which is equal to half a right angle ; by equation ( 1 ) , I = sin2 45 ° + cos2 45 ° . Ι But as the triangle BCP is in this case ( fig . 5 ) a right - angled isosceles triangle , it is evident that sin 45 ° cos 45 ° , and ...
Página 15
... RIGHT - ANGLED TRIANGLES . 1. Relations between the Sides and Angles . - 2 ... triangle , and let AN be measured off upon the hypotenuse , equal in length ... right - angled triangle , either side is equal to the hypotenuse , multiplied ...
... RIGHT - ANGLED TRIANGLES . 1. Relations between the Sides and Angles . - 2 ... triangle , and let AN be measured off upon the hypotenuse , equal in length ... right - angled triangle , either side is equal to the hypotenuse , multiplied ...
Página 16
... RIGHT - ANGLED TRIANGLES . Hany two of the five quantities , a , b , c , A , and 71 , which are independent , be given , the remaining Hunde may be ouloulated . Four cases present them- CASE I. - Given the two sides . CASE II ང་ ས་ ...
... RIGHT - ANGLED TRIANGLES . Hany two of the five quantities , a , b , c , A , and 71 , which are independent , be given , the remaining Hunde may be ouloulated . Four cases present them- CASE I. - Given the two sides . CASE II ང་ ས་ ...
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...