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Rho-Theta methodology is a key component in Area Navigation (RNAV). [1] The term "Rho-Theta" consists of the two Greek letters corresponding to Rho and Theta: [2] [3] [4] Rho (Greek ρ) as a synonym for distance measurement, e.g. Rho would be the equivalent to the English abbreviation "R" for Range
However, some authors (including mathematicians) use the symbol ρ (rho) for radius, or radial distance, φ for inclination (or elevation) and θ for azimuth—while others keep the use of r for the radius; all which "provides a logical extension of the usual polar coordinates notation". [3]
Vectors are defined in cylindrical coordinates by (ρ, φ, z), where . ρ is the length of the vector projected onto the xy-plane,; φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π),
Rho Theta: University of Northern Colorado Active Rho Nu: Western Kentucky University Active Rho Xi: University of Virginia's College at Wise Active Rho Sigma:
theta functions; the angle of a scattered photon during a Compton scattering interaction; the angular displacement of a particle rotating about an axis; the Watterson estimator in population genetics; the thermal resistance between two bodies; ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
For this reason, rho is the least used of the first-order Greeks. Rho is typically expressed as the amount of money, per share of the underlying, that the value of the option will gain or lose as the risk-free interest rate rises or falls by 1.0% per annum (100 basis points).
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :