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To convert between the rectangular and polar forms of a complex number, the conversion formulae given above can be used. Equivalent are the cis and angle notations : z = r c i s φ = r ∠ φ . {\displaystyle z=r\operatorname {\mathrm {cis} } \varphi =r\angle \varphi .}
Alternatively, the conversion can be considered as two sequential rectangular to polar conversions: the first in the Cartesian xy plane from (x, y) to (R, φ), where R is the projection of r onto the xy-plane, and the second in the Cartesian zR-plane from (z, R) to (r, θ).
It addition to standard features such as trigonometric functions, exponents, logarithm, and intelligent order of operations found in TI-30 and TI-34 series of calculators, it also include base (decimal, hexadecimal, octal, binary) calculations, complex values, statistics. Conversions include polar-rectangular coordinates (P←→R), angles.
As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range of 180°, running from 0° to 180°, and does not pose any problem when calculated from an arccosine, but beware for an arctangent.
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. The azimuthal angle is denoted by φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane.
The HP-22S includes many of the typical features found in most scientific calculators: Trigonometric and hyperbolic functions; Polar/rectangular coordinate conversion; Probability functions and statistical calculators (mean and standard deviation, weighted mean, linear regression) Unit and base conversions
Suppose a rectangular xyz-coordinate system is rotated around its z axis counterclockwise (looking down the positive z axis) through an angle , that is, the positive x axis is rotated immediately into the positive y axis. The z coordinate of each point is unchanged and the x and y coordinates transform as above.
The radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if the reference plane is considered horizontal), longitudinal position , [ 1 ] or axial ...