The Elements of Coordinate Geometry
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In our eReader you can find the full English version of the book. Read The Elements of Coordinate Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Elements of Coordinate Geometry
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To quickly assess the difficulty of the text, read a short excerpt:
Find the equation to the chord joining the points on the circle r — 2a cos 6 whose vectorial angles are d^ and 6^, and deduce the equation to the tangent at the point 6^.
The equation to any straight line in polar coordinates is (Art. 88) ^ = rcos((9-a) (1).
If this pass through the points (2a; cos ^j^, 6^ and (2asin^2» ^2)' ^^^ have 2a cos d-^ cos (^j-a)=^ = 2acos ^.3 cos {9.^~a) (2).
Hence cos (2^^ - a) + cos a = cos (2^., - a) + cos a, i.e. 2^1 -a= -(2^0 -a), since d^ and ^2 ^^^ iiot» i'^ ge...neral, equal.
Hence a — d-^ + d.^^ and then, from (2), j? = 2a cos 6-^ cos d.-^.
On substitution in (1), the equation to the required chord is r cos (^ - ^1 - ^2) = 2a cos ^1 cos ^2 (3).
The equation to the tangent at the point d^ is found, as in Art. 150, by putting 6^ = 6^ in equation (3).
We thus obtain as the equation to the tangent rcos (^-2^^) — 2acos2^j^. • As in the foregoing article it could be shewn that the equation to the chord joining the points d^ and 6^ on the circle r= 2a cos {d - 7) is r cos {d -9-^- 6., + 7] — 2a cos {9-^ - 7) cos (9.^ - 7) and hence that the equation to the tangent at the point ^^ is r cos (^ - 2^j + 7) = 2a cos2 (^j - 7).
What to read after The Elements of Coordinate Geometry?
You can find similar books in the "Read Also" column, or choose other free books by S L Sidney Luxton Loney to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Find the equation to the chord joining the points on the circle r — 2a cos 6 whose vectorial angles are d^ and 6^, and deduce the equation to the tangent at the point 6^.
The equation to any straight line in polar coordinates is (Art. 88) ^ = rcos((9-a) (1).
If this pass through the points (2a; cos ^j^, 6^ and (2asin^2» ^2)' ^^^ have 2a cos d-^ cos (^j-a)=^ = 2acos ^.3 cos {9.^~a) (2).
Hence cos (2^^ - a) + cos a = cos (2^., - a) + cos a, i.e. 2^1 -a= -(2^0 -a), since d^ and ^2 ^^^ iiot» i'^ ge...neral, equal.
Hence a — d-^ + d.^^ and then, from (2), j? = 2a cos 6-^ cos d.-^.
On substitution in (1), the equation to the required chord is r cos (^ - ^1 - ^2) = 2a cos ^1 cos ^2 (3).
The equation to the tangent at the point d^ is found, as in Art. 150, by putting 6^ = 6^ in equation (3).
We thus obtain as the equation to the tangent rcos (^-2^^) — 2acos2^j^. • As in the foregoing article it could be shewn that the equation to the chord joining the points d^ and 6^ on the circle r= 2a cos {d - 7) is r cos {d -9-^- 6., + 7] — 2a cos {9-^ - 7) cos (9.^ - 7) and hence that the equation to the tangent at the point ^^ is r cos (^ - 2^j + 7) = 2a cos2 (^j - 7).
What to read after The Elements of Coordinate Geometry?
You can find similar books in the "Read Also" column, or choose other free books by S L Sidney Luxton Loney to read onlineMoreLess
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