Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 4
... Dividing this by r , we obtain , by equation ( 1 ) , The numerical value of a right angle = π . The number 7 , or 1.57079 , which expresses the value of a right angle , referred to this particular angular unit , signifies that this unit ...
... Dividing this by r , we obtain , by equation ( 1 ) , The numerical value of a right angle = π . The number 7 , or 1.57079 , which expresses the value of a right angle , referred to this particular angular unit , signifies that this unit ...
Página 11
... divide the former equation by the latter , we obtain , by equations ( 4 ) and ( 5 ) tan A = cot ( π – A ) , - ( 12 ) If we divide the latter by the former , cot Atan ( π – A ) . ( 13 ) And therefore The tangent of an angle is equal to ...
... divide the former equation by the latter , we obtain , by equations ( 4 ) and ( 5 ) tan A = cot ( π – A ) , - ( 12 ) If we divide the latter by the former , cot Atan ( π – A ) . ( 13 ) And therefore The tangent of an angle is equal to ...
Página 29
... cos 2A : cos 2A COS 2A = I = cos2A - sin3A , - 2 sin❜A , COS 2 A = 2 cos2A - I. ( 14 ) ( 15 ) ( 16 ) If we divide equation ( 9 ) by equation ( 10 ) , we ob- or sin A + sin B sin A sin B tain TRIGONOMETRICAL FORMULA . 29.
... cos 2A : cos 2A COS 2A = I = cos2A - sin3A , - 2 sin❜A , COS 2 A = 2 cos2A - I. ( 14 ) ( 15 ) ( 16 ) If we divide equation ( 9 ) by equation ( 10 ) , we ob- or sin A + sin B sin A sin B tain TRIGONOMETRICAL FORMULA . 29.
Página 30
... divide equation ( 1 ) by ( 2 ) , we obtain sin A cos B + cos A sin B tan ( A + B ) = cos A cos B – sin A sin B - Dividing the numerator and denominator of the right - hand side by cos A cos B , sin A + sin B cos A cos B tan ( A + B ) ...
... divide equation ( 1 ) by ( 2 ) , we obtain sin A cos B + cos A sin B tan ( A + B ) = cos A cos B – sin A sin B - Dividing the numerator and denominator of the right - hand side by cos A cos B , sin A + sin B cos A cos B tan ( A + B ) ...
Página 37
... divide the first of equations ( 7 ) by the first of equations ( 6 ) , we obtain the value of tan A ( Chap . II . ( 4 ) ) , and similarly of tan B and tan C , as follows : tan A √ { ( 8-6 ) ( 8-0 ) } , = { S - b ) s ( 8 a ) c ) ( s 8 ...
... divide the first of equations ( 7 ) by the first of equations ( 6 ) , we obtain the value of tan A ( Chap . II . ( 4 ) ) , and similarly of tan B and tan C , as follows : tan A √ { ( 8-6 ) ( 8-0 ) } , = { S - b ) s ( 8 a ) c ) ( s 8 ...
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
angle is equal angular unit appears from Prop c² 2bc Calculate the value Chap characteristic corres corresponding number cos² cos²A cosecant decimal point degrees and minutes diff equation Euclid expression find the angle find the area Find the log Find the logarithm find the number Find the product Find the quotient Find the sine Find the square find the value five figures following proportion found the mantissa given side Given the logarithm increase of unity integer involution last two figures log cosine log cotangent log sin log tangent Logarithmic Tables mantissa corresponding Multiply the tabular natural sines number is equal proceed by RULE PROPOSITION radius rence required to find right-angled triangle rule appears secant sect semiperimeter sin² sin²A sines and cosines square root subtends subtract Tables of Natural tables the corresponding tabular difference three figures triangle BCP
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.