The Americana; a universal reference library, comprising the arts and sciences, literature, history, biography, geography, commerce, etc., of the world . formute of transforma-tion are found by adding h sin to and k sin enrespectively to the right-hand members of theforegoing equations. Most commonly the axesare assumed to be rectangular. In that case,w=9o°, sin a/ = i, ^ = (go° + a), and the equa-tions of transformation become: ;c=a:cos a —ysina-f-^, y=.xsin a+cos a + k. The equa-tions for effecting the inverse transformation are found by solving for x and y the equationsof the direct transfo
The Americana; a universal reference library, comprising the arts and sciences, literature, history, biography, geography, commerce, etc., of the world . formute of transforma-tion are found by adding h sin to and k sin enrespectively to the right-hand members of theforegoing equations. Most commonly the axesare assumed to be rectangular. In that case,w=9o°, sin a/ = i, ^ = (go° + a), and the equa-tions of transformation become: ;c=a:cos a —ysina-f-^, y=.xsin a+cos a + k. The equa-tions for effecting the inverse transformation are found by solving for x and y the equationsof the direct transformation. Polar Coordinates.—Though it is never neces-sary, it is often convenient, to employ otherthan Cartesian coordinates to determine theposition of a point. Of such other coordinatesystems, the most familiar is the polar. Aboutany point O (as center), called the pole, supposedrawn all possible concentric circles; alsosuppose drawn out from the pole all possiblerays (half-lines). Any circle and any raydetermine (intersect in) a point, and all pointsof the plane are thus determined; conversely,any point determines (is common to) a circle. —X Fig. 3- and a ray, and all pairs of such lines (circle an^ray) are thus determined. A circle is givenby its radius p, and a ray by its angle d madewith a fixed ray. as OQ. called the initial lineor polar axis. All the circles are obtained byletting p vary from o to m , and all rays byallowing 0 to vary from o to 2it or 360°. Ob-viously, to any pair of values (within the rangesof variation mentioned) of p and 6 there corre-sponds one point, and conversely. The pairof numbers {p, 8) determining or determinedby a point P are called the polar coordinatesof P. In particular, p is called the radiusvector, and 0 the vectorial angle, of P. Transformations from Cartesian to Polar Coor-dinates.—We present here only the simplest andmost important case, viz., that wherein theCartesian axes are rectangular, the origincoinciding with the po
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Keywords: ., bookcentury1900, bookdecade1900, booksubjectencyclo, bookyear1908
