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Converting Coordinates between Rectangular and Polar

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Introduction

Entering an ordered pair on a two dimensional graph (including imaginary numbers) can be done in either of two ways.
  • Rectangular or Cartesian coordinates
  • Polar or Cylindrical coordinates
The instructions in this document explain how to enter ordered pairs using both rectangular and polar notations. The instructions will demonstrate how to convert between the two notations. In addition, instructions on adding and subtracting the ordered pairs are included.
NOTE: Decimal number format is set at Fixed 2 decimal placement.
Ordered pairs are set between parentheses. The difference between entering a rectangular coordinate and a polar coordinate is that rectangular coordinates are separated by a comma, while polar or cylindrical coordinates are separated by an angle symbol.

Examples

To set the coordinate mode, enter the Modes screen and select the notation desired.
For example, enter (12,5) on the calculator display, then press ENTER.
  • If the Coord System is rectangular, the item will not change.
  • If your Coord System is polar, the calculator will convert (12,5) to (13 ANGLE 22.62).
    NOTE: The calculator stores in rectangular mode, and calculations are based on this internal rectangular representation. However, the display will show whatever coordinate mode is selected in the Coord System field.

Example

Select the Modes screen of the calculator. Set the Coord System to Rectangular and the Angle Measure to Degrees. In this document, the word "ANGLE" represents the angle symbol.
NOTE: The angle symbol on an HP 48g calculator is accessed by pressing Right-Shift, then SPC, and on an HP 49g, by pressing ALPHA, Right-Shift, then 6.
In RPN entry mode
  1. Type (3,4), then press ENTER. (3,4) will be displayed on the screen.
  2. Now type in (5 ANGLE 30), and press ENTER. (4.33, 2.5) will be displayed, because Coord System is set to Rectangular.
  3. Press the addition (+) key. The two items on the stack equal (7.33, 6.5).
  4. To convert to Polar mode, enter the Modes screen and change the Coord System to Polar. The items on the stack will automatically change to Polar mode. The display will read (9.797 ANGLE 41.565).
  5. Type (3,4), then press ENTER. The calculator converts the rectangular notation to polar notation, because the Coord System is set to Polar. (5 ANGLE 53.13) is displayed on the screen.
  6. Press the subtraction (-) key. (5 ANGLE 30) is displayed on the screen.
In Algebraic entry mode
  1. Type in (3,4), then press ENTER. Notice that when this number goes onto the stack it remains the same.
  2. Now type in (5 ANGLE 30), and press ENTER. The calculator will display (4.33, 2.5). Notice that it appears in rectangular mode because Coord System is set to Rectangular.
  3. Arrow up to highlight (3,4), on the right side of the display, then press ENTER. Press the addition (+) key, Left Shift, ANS, then ENTER. (7.33, 6.5) is displayed on the screen.
  4. To convert to polar mode, enter the Modes screen and change the Coord System to Polar. The item on stack level one will automatically change to polar mode. (9.80 ANGLE 41.57) is displayed on the screen.
  5. Type in (3,4), then press ENTER. Notice that the calculator converted the rectangular notation to polar notation, because the Coord System is set to Polar. (5 ANGLE 53.13) is displayed on the screen.
  6. Arrow up and highlight (9.80 ANGLE 41.57), on the right side of the display, press ENTER. Press the subtraction (-) key, Left Shift, ANS, then ENTER. (5 ANGLE 30) is displayed on the screen.
  7. Enter the Modes screen and change the Coord System to Rectangular. Return to the stack, the rectangular coordinates (4.33,2.5) are displayed on the screen.

Helpful hint

Typing RECT or CYLIN directly on the stack will change the setting without entering the Modes screen. RECT equals rectangular mode and CYLIN equals cylindrical or polar mode.

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