Inscribed angle its intersection points equals half of the central angle subtended by the chord. See also Tangent lines to circles. The inscribed angle theorem is used in many proofs of elementary Euclidean geometry of the plane. A special case of the theorem is Thales' theorem, which states that the angle subtended by a diameter is always 90°, i.e., a right angle. As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle. As another example, the inscribed angle theorem is the basis for several
Small-angle approximation approximately 60 degrees. The formulas for addition and subtraction involving a small angle may be used for interpolating between trigonometric table values: Example: sin(0.755) Small-angle approximation The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero. They are truncations of the Taylor series for the basic trigonometric functions to a second-order approximation. This truncation gives: where is the angle in radians. The small angle approximation is useful in many areas of engineering and physics, including mechanics, electromagnetics, optics (where it forms the basis of the paraxial