Eccentric angle

Japanese: 離心角 - りしんかく（英語表記）eccentric angle

(1) If an ellipse is expressed in a Cartesian coordinate system with its center at the origin O and its major axis as the x- ^axis , it can be expressed as an equation of the form ( x / a ) ² + ( y / b ) ² = 1 , in which case the circle x2 + y2 = ^a2 is called the auxiliary circle of the ellipse. Now, if there is a point P on the circumference of the ellipse, let Q be the point in the same quadrant ^as P where a line drawn through P perpendicular to the x- axis intersects with the auxiliary circle, and let φ be the angle that the half line OQ makes with the positive direction of the x- axis, then the coordinates ( x , y ) of P can be expressed as x = a cosφ, y = b sinφ.

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

(1)楕円は，その中心を原点Oとしその長軸をx軸とする直交座標系を用いれば，(x/a)²＋(y/b)²＝1という形の方程式で表されるが，このとき円x²＋y²＝a²を楕円の補助円という。いま，楕円の周上に点Pがあるとき，Pを通ってx軸に垂直にひいた直線が補助円と交わる点のうちPと同じ象限にあるものをQとし，半直線OQがx軸の正の方向となす角をφとすれば，Pの座標(x,y)はx＝acosφ，y＝bsinφで表される。

出典　株式会社平凡社世界大百科事典第２版について　情報

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