Manual of plane trigonometry, by J.A. Galbraith and S. Haughton |
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Página 7
... tangents to the circle at A and D respectively , and cutting the line CB produced in T and S , then The line BP is the sine of the angle ACB . CP cosine 99 " " " " AT " " 99 tangent 99 99 CT " 9 secant 99 99 99 DS " " cotangent 99 CS ...
... tangents to the circle at A and D respectively , and cutting the line CB produced in T and S , then The line BP is the sine of the angle ACB . CP cosine 99 " " " " AT " " 99 tangent 99 99 CT " 9 secant 99 99 99 DS " " cotangent 99 CS ...
Página 11
... tangent of an angle is equal to the cotangent of its complement . The cotangent of an angle is equal to the tangent of its complement . The relation between the sines and cosines of supplemental angles may be expressed by the equa ...
... tangent of an angle is equal to the cotangent of its complement . The cotangent of an angle is equal to the tangent of its complement . The relation between the sines and cosines of supplemental angles may be expressed by the equa ...
Página 12
... tangent , & c . of the angle 45 ° , which is equal to half a right angle ; by equation ( 1 ) , I = sin3 45 ° + cos3 45 ° . But as the triangle BCP is in this case ( fig . 5 ) a right - angled isosceles triangle , it is evident that sin ...
... tangent , & c . of the angle 45 ° , which is equal to half a right angle ; by equation ( 1 ) , I = sin3 45 ° + cos3 45 ° . But as the triangle BCP is in this case ( fig . 5 ) a right - angled isosceles triangle , it is evident that sin ...
Página 13
... tangents , secants , & c . , of every de- gree and minute in the quadrant are registered . The statement of the method by which such tables are constructed is unsuited to the present treatise ... tangent of TRIGONOMETRICAL MAGNITUDES . 13.
... tangents , secants , & c . , of every de- gree and minute in the quadrant are registered . The statement of the method by which such tables are constructed is unsuited to the present treatise ... tangent of TRIGONOMETRICAL MAGNITUDES . 13.
Página 14
... tangent of 30 ° . Ans . tan 30 ° = 0.57735 . 4. Calculate the sine and cosine of 120 ° . As 120 ° is the supplement of 60 ° , it follows from sect . 3 , that = 0.86602 , Ans . sin 120 ° = sin 60 ° COS 120 ° - cos 60 ° 0.50000 . 5 ...
... tangent of 30 ° . Ans . tan 30 ° = 0.57735 . 4. Calculate the sine and cosine of 120 ° . As 120 ° is the supplement of 60 ° , it follows from sect . 3 , that = 0.86602 , Ans . sin 120 ° = sin 60 ° COS 120 ° - cos 60 ° 0.50000 . 5 ...
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.