HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 52

The coordinate system selection affects the way vectors and complex numbers are displayed and entered. To learn more about complex numbers and vectors, see Chapters 4 and 9, respectively. Two- and three-dimensional vector components and complex numbers can be represented in any of 3 coordinate systems: The Cartesian (2 dimensional) or Rectangular (3 dimensional), Cylindrical (3 dimensional) or Polar (2 dimensional), and Spherical (only 3 dimensional). In a Cartesian or Rectangular coordinate system a point P will have three linear coordinates (x,y,z) measured from the origin along each of three mutually perpendicular axes (in 2 d mode, z is assumed to be 0). In a Cylindrical or Polar coordinate system the coordinates of a point are given by (r,θ,z), where r is a radial distance measured from the origin on the xy plane, θ is the angle that the radial distance r forms with the positive x axis -- measured as positive in a counterclockwise direction --, and z is the same as the z coordinate in a Cartesian system (in 2 d mode, z is assumed to be 0). The Rectangular and Polar systems are related by the following quantities: x = r ⋅ cos(θ ) r = x2 + y2 y = r ⋅ sin(θ ) θ = tan −1   y x   z= z In a Spherical coordinate system the coordinates of a point are given by (ρ,θ,φ) where ρ is a radial distance measured from the origin of a Cartesian system, θ is an angle representing the angle formed by the projection of the linear distance ρ onto the xy axis (same as θ in Polar coordinates), and φ is the angle from the positive z axis to the radial distance ρ. The Rectangular and Spherical coordinate systems are related by the following quantities: x = ρ ⋅ sin(φ ) ⋅ cos(θ ) ρ = x2 + y2 + z2 y = ρ ⋅ sin(φ ) ⋅ sin(θ ) θ = tan −1 y   x z = ρ ⋅ cos(φ ) φ = tan −1    x 2 + y 2  z  To change the coordinate system in your calculator, follow these steps: Page 1-23