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In geometry, a trapezoid (/ ˈ t r æ p ə z ɔɪ d /) in North American English, or trapezium (/ t r ə ˈ p iː z i ə m /) in British English, [1] [2] is a quadrilateral that has at least one pair of parallel sides.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: (). The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area.
Any square, rectangle, isosceles trapezoid, or antiparallelogram is cyclic. A kite is cyclic if and only if it has two right angles – a right kite.A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral that is also ex-tangential.
Trapezium, plural trapezia, may refer to: Trapezium, in British and other forms of English, a trapezoid, a quadrilateral that has exactly one pair of parallel sides; Trapezium, in North American English, an irregular quadrilateral with no sides parallel; Trapezium (bone), a bone in the hand; Trapezium Cluster, a group of stars in the Orion Nebula
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Similarly, the angle that a line makes with the horizontal can be defined by the formula = (), where m is the slope of the line. In three dimensions, distance is given by the generalization of the Pythagorean theorem: d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 , {\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2 ...