Analytic Geometry for Technical Schools And Colleges
The book Analytic Geometry for Technical Schools And Colleges was written by author Preston Albert Lambert Here you can read free online of Analytic Geometry for Technical Schools And Colleges book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Analytic Geometry for Technical Schools And Colleges a good or bad book?
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Let the pole A' referred to the rectangular coordinates be (m, n), 6' the angle made by the polar axis with the X-axis. Then X = AD = m + r cos (6 + 6'), y = PD = n + r sin (d + 6'). When the pole is at the origin, and the polar axis coincides with the X-axis, these formulas be- come X = r cos 6, y — r sin $. If the polar equation of a geometric figure is given and the rectangular equation is desired, find the values of the polar coordinates r and 6 of any point in terms of the rectan- 80 ANALY...TIC GEOMETRY gular coordinates x and y of the same point ; substitute in the polar equsition F(r, 6) = 0, and the resulting equation /(a;, ?/)=:0 is the rectangular equation of the curve. From the figure X — m r = y/{x - my +{y- w)^ cos (6 + 6') = sin(^ + ^')- •'~'" ^{x - mf + (2/ - ?0' V(. X'-m/+(y-n)^ When the origin is at the pole, and the X-axis coincides with the polar axis, these formulas become r — V. V- + ]j\ cos Q = ^ sin 9 = • VaT- + y- Var + y- Problems. — Transform from rectangular coordinates to polar, pole at origin, polar axis coinciding with A'-axis, and plot the locus from both equations.
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