|
In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted ''S''1; the generalization to higher dimensions is the unit sphere. If (''x'', ''y'') is a point on the unit circle's circumference, then |''x''| and |''y''| are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, ''x'' and ''y'' satisfy the equation : Since ''x''² = (−''x'')² for all ''x'', and since the reflection of any point on the unit circle about the ''x''- or ''y''-axis is also on the unit circle, the above equation holds for all points (''x'', ''y'') on the unit circle, not only those in the first quadrant. The interior of the unit circle is called the open unit disk, while the interior of the unit circle combined with the unit circle itself is called the closed unit disk. One may also use other notions of "distance" to define other "unit circles", such as the Riemannian circle; see the article on mathematical norms for additional examples. ==In the complex plane== The unit circle can be considered as the unit complex numbers, i.e., the set of complex numbers ''z'' of the form : for all ''t''. This relation is Euler's formula. In quantum mechanics, this is referred to as phase factor. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「unit circle」の詳細全文を読む スポンサード リンク
|