A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous ExamplesD.C. Heath & Company, 1892 - 368 páginas |
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Página 57
... Dividing the first of the ' x , y ' formulæ by the second , we have , by Art . 23 , tan ( x + y ) sin ( x + y ) = cos ( x + y ) = sin x cos y + cosa sin y cos x cos y sin x siny Dividing both terms of the fraction by cos x cos y , sin x ...
... Dividing the first of the ' x , y ' formulæ by the second , we have , by Art . 23 , tan ( x + y ) sin ( x + y ) = cos ( x + y ) = sin x cos y + cosa sin y cos x cos y sin x siny Dividing both terms of the fraction by cos x cos y , sin x ...
Página 59
... Dividing ( 1 ) by ( 2 ) , and reducing by dividing both terms . of the fraction by cos x cos y cos z , we get tan ( x + y + 2 ) = 1 tan x + tany + tanz - tan x tan y tan z - - tan x tany — tany tanz - tanz tan x ( 3 ) EXAMPLES . 1 ...
... Dividing ( 1 ) by ( 2 ) , and reducing by dividing both terms . of the fraction by cos x cos y cos z , we get tan ( x + y + 2 ) = 1 tan x + tany + tanz - tan x tan y tan z - - tan x tany — tany tanz - tanz tan x ( 3 ) EXAMPLES . 1 ...
Página 60
... ( 4 ) , and dividing it into ( 1 ) , we have sin 2 x 1+ cos 2 x = : tan . ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) NOTE.- These seven formulæ are very important . ---- The 60 PLANE TRIGONOMETRY . Functions of Double Angles.
... ( 4 ) , and dividing it into ( 1 ) , we have sin 2 x 1+ cos 2 x = : tan . ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) NOTE.- These seven formulæ are very important . ---- The 60 PLANE TRIGONOMETRY . Functions of Double Angles.
Página 89
... divide 371.49 by 52.376 , we pro- ceed thus : log10 371.49 2.56995 = log 10 52.376 = 1.71913 0.85082 which is the logarithm of 7.092752 , the quotient required . 3. If we have to find the fourth power of PROPERTIES OF LOGARITHMS . 89.
... divide 371.49 by 52.376 , we pro- ceed thus : log10 371.49 2.56995 = log 10 52.376 = 1.71913 0.85082 which is the logarithm of 7.092752 , the quotient required . 3. If we have to find the fourth power of PROPERTIES OF LOGARITHMS . 89.
Página 94
... = log , m log , 125 log , m 55 3 Show how to transform 2. Logarithms with base 2 to logarithms with base 8 . Ans . Divide each logarithm by 3 . 3. Logarithms with base 9 to logarithms with base 3 94 PLANE TRIGONOMETRY .
... = log , m log , 125 log , m 55 3 Show how to transform 2. Logarithms with base 2 to logarithms with base 8 . Ans . Divide each logarithm by 3 . 3. Logarithms with base 9 to logarithms with base 3 94 PLANE TRIGONOMETRY .
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Otras ediciones - Ver todas
A Treatise on Plane and Spherical Trigonometry: And Its Applications to ... Edward Albert Bowser Sin vista previa disponible - 2013 |
Términos y frases comunes
algebraically angle AOP angle of elevation base calculate centre circle circular measure common logarithms cos b cos cos² cosec cotangent decimal places denote diff equal equations EXAMPLES expression feet find log find the angle find the height find the number formulæ Given log Hence horizon hypotenuse integer log cot log sin log sine mantissa Multiply negative number whose logarithm observed obtained opposite perpendicular plane polar triangle positive Prove the following quadrant R₁ r₂ radian radius right angles right triangle sec² secant sides Similarly sin a cos sin B sin sin x sin² sin³ sines and cosines sinx siny solution Solve spherical triangle subtends table of logarithms table of natural tan² tangent triangle ABC trigonometric functions vertical yards ОР
Pasajes populares
Página 148 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 147 - Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles.
Página 278 - AB'C, we have by (4) cos a' — cos b cos c' + sin b sin c' cos B'AC, or cos(тг— a) = cos b cos(тг— c) + sin b sin(тт — C)COS(тг —A). .-. cos a = cos b cos с + sin b sin с cos A.
Página 278 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 278 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 17 - If the cosine of A be subtracted from unity, the remainder is called the versed sine of A. If the sine of A be...
Página 89 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 149 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.