Math Trigonometry Unit Circle Rotation Sign Indication

In mathematics, the angle of rotation is a measurement of the amount, of namely

angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles ...

, that a figure is rotated about a fixed point, often the

center Center or centre may refer to: Mathematics *Center (geometry), the middle of an object * Center (algebra), used in various contexts ** Center (group theory) ** Center (ring theory) * Graph center, the set of all vertices of minimum eccentricity ...

of a

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

. A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310° (counterclockwise) can also be called a rotation of –50° (since , a full

turn Turn may refer to: Arts and entertainment Dance and sports * Turn (dance and gymnastics), rotation of the body * Turn (swimming), reversing direction at the end of a pool * Turn (professional wrestling), a transition between face and heel * Turn, ...

). A counterclockwise rotation of more than one complete turn is normally measured

modulo In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is t ...

360°, meaning that 360° is subtracted off as many times as possible to leave a non-negative measurement less than 360°. For example, the carts on a

Ferris wheel A Ferris wheel (also called a Giant Wheel or an observation wheel) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, gondolas, capsule ...

move along a circle around the center point of that circle. If a cart moves around the wheel once, the angle of rotation is 360°. If the cart was stuck halfway, at the top of the wheel, at that point its angle of rotation was only 180°. Angles are commonly measured in

degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathemati ...

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...

s, gons (gradians) and turns, sometimes also in

angular mil A milliradian ( SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting ...

s and

binary radian The terms binary angular measurement (BAM) and binary angular measurement system (BAMS) refer to certain methodologies for representing and manipulating angles using binary ( base 2) fixed-point arithmetic. The unit of angular measure used in th ...

s. They are central to

polar coordinates In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to t ...

and

trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...

Properties

If the angle of rotation is denoted as AOR(), *

AOR(360a+b)=AOR(b)

for all integers ''a'' and real values ''b''.

Properties

See also