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Libros Libros 1 a 10 de 23 sobre Put x = x cos 0 — y sin 0, y = x
" Put x = x cos 0 — y sin 0, y = x "
A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ... - Página 227
de Isaac Todhunter - 1858 - 316 páginas
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A treatise on plane co-ordinate geometry

Isaac Todhunter - 1855 - 299 páginas
...shortness. 271. We may suppress the accents on the variables in (4) of the preceding article and write it This equation we shall further simplify by changing...0 + y' cos 0, and substitute in (5) ; thus a;'2 (a cos20 + c sin20 + b sin 0 cos 0) + y'*(a sin2 0 + c cos2 0 - b sin 0 cos 0) + x'y' [2 (c - a) sin 0...
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A treatise on plane co-ordinate geometry

1855 - 299 páginas
...suppress the accents on the variables in (4) of the preceding article and write it ea? + Ixy + cy2 +f = 0 (5). This equation we shall further simplify by...axes. (Art. 81.) Put x — x cos 0 — y sin 0, y = x sin0 + y' cos 0, and substitute in (5) ; thus x'2 (a cos20 + c sin2!? + b sin 0 cos 0) + y'2 (a sin2...
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Elements of Plane Analytic Geometry, Volumen 25

John Daniel Runkle - 1888 - 344 páginas
...axes, in which 0 denotes the angle which the new axis of X makes with the old one, are (Art. 21, c) x = x' cos 0 — y' sin 0, y = x' sin 0 + y' cos 0. Substitute these values of x and y in 8 = 0, and it becomes, omitting primes, and reducing, (A cos2...
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The Collected Mathematical Papers of Arthur Cayley, Volumen 11

Arthur Cayley - 1896 - 643 páginas
...0 + 0" sin 0 - xlt y' =/3' + a", »C — ft — £J * Hence Xi = x' cos 0 + y' sin 0, or .r' = #,' cos 0 — y,' sin 0, y/ = — x' sin 0 + y' cos 0, y' = #,' sin 0 + y\ cos 0, values which give a;'2 + y'2 = a;/2 + y/'2, which equation expresses that...
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A Treatise on the Mathematical Theory of Elasticity

Augustus Edward Hough Love - 1906 - 551 páginas
...substitution which corresponds with rotation through an angle 0 about the axis of z is given by the equations x = x cos 0 + y sin 0, y' = — x sin 0 + y cos 0, z' = z ; (3) and the formulae that connect the components of strain referred to the two systems of...
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Analytic Geometry, a First Course

William Henry Maltbie - 1906 - 142 páginas
...we have Oa cos Y + aP cos 0 = Oc cos and these two equations at once reduce to - — 0 + cP cos 0, x = x cos 0 — y' sin 0 y = x sin 0 + y cos 0 which are the desired formulae of transformation. *If an equation of the second degree has no terms...
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Plane Analytic Geometry: With Introductory Chapters on the Differential Calculus

Maxime Bôcher - 1915 - 235 páginas
...90°) = «/' cos 0. Hence, applying to the broken line OM' P the principle of § 2, we find ' fx = x' .cos 0 — y' sin 0, [ y = x' sin 0 + y cos ,0, and these are the formulae for expressing the old coordinates in terms of the new. The formulae for expressing...
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Plane Analytic Geometry: With Introductory Chapters on the Differential Calculus

Maxime Bôcher - 1915 - 235 páginas
...can be found either by solving the equations (1) for x', y', or directly from the figure. They are (x' = x cos 0 + y sin 0, } y' = — x sin 0 + y cos 9. The general transformation from one system of rectangular coordinates to another will be one in...
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Elementary Mathematical Analysis

John Wesley Young, Frank Millett Morgan - 1917 - 548 páginas
...y sin 0, y' = x sin 8 + y cos 0. Solving these equations for x and y in terms of x', y', we obtain x - x' cos 0 + y' sin 0, * ' y = — x' sin 0 + y' cos 0. If P(x, y) satisfies equation (20), P*(x', y') will satisfy the equation obtained by substituting the...
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NASA technical note

1976
...1 and 2, the following relationships can be written between inates in the image and object planes: x = x cos 0 + y sin 0 y = -x sin 0 + y cos 0 X = X cos 4> - Y sin $ Y = X sin 4> + Y cos $ X — XQ X — XQ f cos 6 - (y - yp) sin 9 y - yp (Y...
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