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Parametric Graphing

CalcES supports draw parametric function with x and y parameters.

For example:

x = Sin(2t)
y = Cos(t)
Graph of Sin(2t):Cos(t)

Steps to draw parametric graph

Syntax:

x(t):y(t)
    1. To enter t variable, press ALPHA Ln
    1. To enter colon : symbol, press ALPHA ∫dx
Enter Sin(2t):Cos(t)

Tap the GRAPH button to draw parametric graph

Parametric graph of Sin(2t):Cos(t)

Working with parametric graphs

The CALC panel: calculate value a point

The Calc panel allow you to calculate the value of x(t):y(t) with given t value. Press Calc button to open Calc panel:

Press `Calc` button to open `Calc` panel

Tap the Edit icon to enter the value of t

Tap the **Edit** icon

After entering value of t, the panel displays some properties at t:

x = ?
y = ?
dx/dt = ?
dy/dt = ?
dy/dx = ?
Properties of Sin(2t):Cos(t) at t = 3.28

The TABLE panel: generate table of values

The Table panel allow you to generate a table of values. Tap the Table button to open it:

Press `Table` button

Here is the table of values of Sin(2t):Cos(t) with Δt=1, and start at 0

Press `Calc` button to open `Calc` panel

To change the Δt or the Start value, tap the edit icon on the left of Δt:

Tap the edit icon on the left of `Δt`

Tap the edit icon to change value of Start and Step:

Table start and step settings dialog

Example, Start=0.5 and Step=0.25

Table start and step settings dialog

Tap Save to recalculate the table:

Table of values of Sin(2t):Cos(t)

Settings the t range

The default range of t variable is from -10 to 10, to change this value:

  • Open the settings screen:
Tap gear icon to open settings screen
  • Select the Graph tab
The graph settings tab
  • Scroll to the Parametric graph section:
The parametric graph setting section
  • Change the Parametric start and Parametric stop with your value, tap OK to save
Parametric start editor

Example:

x=sin(2t)+3sin(t)
y=2sin(3t)
Enter sin(2t)+3sin(t):2sin(3t)
  • For the range of t from 0 to Pi
Graph of sin(2t)+3sin(t):2sin(3t) from 0 to Pi
  • For the range of t from -Pi to Pi
Graph of sin(2t)+3sin(t):2sin(3t) from -Pi to Pi
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