Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 6
... Relations of Trigo- nometrical Magnitudes . - 3 . Complemental and Supplemental An- gles . - 4 . Trigonometrical Tables . DEFINITION OF TRIGONOMETRICAL MAGNITUDES . 1. THERE are certain magnitudes connected with angles , and entering ...
... Relations of Trigo- nometrical Magnitudes . - 3 . Complemental and Supplemental An- gles . - 4 . Trigonometrical Tables . DEFINITION OF TRIGONOMETRICAL MAGNITUDES . 1. THERE are certain magnitudes connected with angles , and entering ...
Página 7
... RELATIONS OF TRIGONOMETRICAL MAGNITUDES . 2. The relations which these magnitudes have to each other are derived from geometrical principles as follows . Because the triangles BCP , ACT , and CDS are right - angled , it follows ( Euclid ...
... RELATIONS OF TRIGONOMETRICAL MAGNITUDES . 2. The relations which these magnitudes have to each other are derived from geometrical principles as follows . Because the triangles BCP , ACT , and CDS are right - angled , it follows ( Euclid ...
Página 10
... relations exist between the sines and cosines of complemental angles : The sine of an angle is equal to the cosine of its complement . The cosine of an angle is equal to the sine of its complement . Let ACB be any angle , and ACE ( fig ...
... relations exist between the sines and cosines of complemental angles : The sine of an angle is equal to the cosine of its complement . The cosine of an angle is equal to the sine of its complement . Let ACB be any angle , and ACE ( fig ...
Página 11
... relation between the sines and cosines of complemental angles may be thus expressed : sin A = cos ( π – A ) , cos A = sin ( -A ) . ( 10 ) ( 11 ) If we divide the former equation by the latter , we obtain tan Acot ( -A ) , If we divide ...
... relation between the sines and cosines of complemental angles may be thus expressed : sin A = cos ( π – A ) , cos A = sin ( -A ) . ( 10 ) ( 11 ) If we divide the former equation by the latter , we obtain tan Acot ( -A ) , If we divide ...
Página 15
... Relations between the Sides and Angles . - 2 . Four Cases of Right- Angled Triangles . - 3 . The Four Cases computed by Logarithmic Tables . RELATIONS BETWEEN THE SIDES AND ANGLES . 1. LET ABC ( fig . 8 ) be a right - angled triangle ...
... Relations between the Sides and Angles . - 2 . Four Cases of Right- Angled Triangles . - 3 . The Four Cases computed by Logarithmic Tables . RELATIONS BETWEEN THE SIDES AND ANGLES . 1. LET ABC ( fig . 8 ) be a right - angled triangle ...
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
already angle is equal angular unit appears applying Book Calculate called centre Chap characteristic circle Circumference complement computation corresponding cos² cosec cotangent decimal degrees and minutes derived diameter diff divide equation Euclid EXAMPLES Express feet figures find the angle find the area Find the logarithm find the number Find the product find the value follows Given the logarithm greater half increase length less log cosine log sin log sine Logarithmic Tables magnitudes mantissa means measured miles minutes Multiply negative obtain opposite Prop proportional PROPOSITION quantities radius ratio reason relations required to find respectively result right angle right-angled triangle root rule secant seconds sect side similar sin² sines and cosines square root Substituting subtends subtract supplement tables tangent triangle BCP trigonometrical unity
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...