Central angle intersection points and of the legs of the angle with the circle form a diameter, then is a straight angle. (In radians, .) Let be the minor arc of the circle between points and , and let be the radius of the circle. If the central angle is subtended by , then If the central angle is not subtended by the minor arc , then is a reflex angle and If a tangent at and a tangent at intersect at the exterior point , then denoting the center as , the angles (convex) and are supplementary (sum to 180°). A
Hyperbolic angle identities use the number "i" to remove the alternating factor (−1) from terms of the series to restore the full halves of the exponential series. Nevertheless, in the theory of holomorphic functions, the hyperbolic sine and cosine functions are incorporated into the complex sine and cosine functions. Hyperbolic angle In mathematics, a hyperbolic angle is a geometric figure that defines a section of a hyperbola. The relationship of a hyperbolic angle to a hyperbola parallels the relationship of an "ordinary" angle to a circle. Hyperbolic angle is defined in terms of the "standard" rectangular hyperbola: "y" = 1/"x", for positive