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 4
... become greater than an angle of four right angles . Thus , when OP coincides with the lines OB , OA ' , OB ' , OA , in the second revolution , the angles described , measured from the beginning of the first revolution , are angles of ...
... become greater than an angle of four right angles . Thus , when OP coincides with the lines OB , OA ' , OB ' , OA , in the second revolution , the angles described , measured from the beginning of the first revolution , are angles of ...
Página 5
... become of any magnitude whatever . In the same way OP may revolve in the negative direc- tion about O any number of times , generating a negative angle ; and this negative angle may obviously have any magnitude whatever . The angle AOP ...
... become of any magnitude whatever . In the same way OP may revolve in the negative direc- tion about O any number of times , generating a negative angle ; and this negative angle may obviously have any magnitude whatever . The angle AOP ...
Página 21
... become the modern functions of the angle which the arc subtends at the centre . If , therefore , the radius be taken as unity , the old functions of the arc AP become the modern functions of the angle AOP . Thus , representing the arc ...
... become the modern functions of the angle which the arc subtends at the centre . If , therefore , the radius be taken as unity , the old functions of the arc AP become the modern functions of the angle AOP . Thus , representing the arc ...
Página 27
... becomes negative and decreases algebraically from zero to 1 ; therefore tan 180 ° = 0 . Hence in the 2d quadrant tan A is negative , and increases algebraically from to 0 . - - co When A passes into the 2d quadrant , and is only just ...
... becomes negative and decreases algebraically from zero to 1 ; therefore tan 180 ° = 0 . Hence in the 2d quadrant tan A is negative , and increases algebraically from to 0 . - - co When A passes into the 2d quadrant , and is only just ...
Página 53
... becomes ( 1 ) cos { 90 ° - ( x + y ) } = cos ( 90 ° - x ) cos y + sin ( 90 ° - x ) siny . ( Art . 29 ) .. sin ( x + y ) = sin x cos y + cos x sin y . The student should make the substitutions indicated below , and satisfy himself that ...
... becomes ( 1 ) cos { 90 ° - ( x + y ) } = cos ( 90 ° - x ) cos y + sin ( 90 ° - x ) siny . ( Art . 29 ) .. sin ( x + y ) = sin x cos y + cos x sin y . The student should make the substitutions indicated below , and satisfy himself that ...
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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.