Analytic Geometry, a First Course

Cover Analytic Geometry, a First Course
Analytic Geometry, a First Course
Maltbie, William Henry, 1867-
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Let P be any point (x, y) in the plane.
Then by considering the projections of OaP and OcP on OX and OY we have x = x cos a + y cos P y = x sin a + y sin P, fio. 13.
a set of formulae which are sufficient to transform from any set of rectangular axes to any set of oblique axes which have the same origin.
If we wish to transform from oblique to rectangular axes we have only to solve the formulae just derived for x and y and we have / _ x sin P — // cos P sin 8 f __ — x sin a + y cos a sin 8 1. F
...ree the equation PROBLEMS.
2x — 3t/ + l = from its term in y by a change in the direction of the Y axis.
2. What form does the equation x 2 + y 2 = r 2 take when the X axis is left unchanged but the Y axis moved so that the angle between the axes is 30° ?
Analytic Geometry. 43 32. To change the last of our assumptions CHANGE OF THE without affecting any of the others it is scales of sufficient to write MEASUREMENT.
X = Kx The effect is evidently to multiply the unit of measurement on the X axis by K and on the Y axis by L.


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