Degree (angle)A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2pi radians, one degree is equivalent to pi/180 radians. The original motivation for choosing the degree as a unit of rotations and angles is unknown.
Arc lengthArc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. A rectifiable curve has a finite number of segments in its rectification (so the curve has a finite length). If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) , then the curve is rectifiable (i.
Angular frequencyIn physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves). Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity. Angular frequency can be obtained multiplying rotational frequency, ν (or ordinary frequency, f) by a full turn (2π radians): ω=2π radν.
GradianIn trigonometry, the gradian, also known as the gon (from gōnía), grad, or grade, is a unit of measurement of an angle, defined as one hundredth of the right angle; in other words, there are 100 gradians in 90 degrees. It is equivalent to 1/400 of a turn, 9/10 of a degree, or pi/200 of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement, initiated as part of metrication and decimalisation efforts.
Rate (mathematics)In mathematics, a rate is the quotient of two quantities in different units of measurement, often represented as a fraction. If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change in the other (dependent) variable. One common type of rate is "per unit of time", such as speed, heart rate, and flux.
Solid angleIn geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the apex of the solid angle, and the object is said to subtend its solid angle at that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).
RadianThe 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. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit, defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as .
Sine and cosineIn mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted simply as and .
MilliradianA 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 the angle of the sight compared to the barrel (up, down, left, or right). Milliradians are also used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances.
Unit circleIn mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S1 because it is a one-dimensional unit n-sphere. If (x, y) is a point on the unit circle's circumference, then and are the lengths of the legs of a right triangle whose hypotenuse has length 1.
