Parametric Graphing

CalcES supports draw parametric function with x and y parameters.

Example

x=Sin(2t)
y=Cos(t)

Steps to draw parametric graph

Syntax:

x(t):y(t)

Note

1. To enter t variable, press ALPHA Ln
2. To enter colon : symbol, press ALPHA ∫dx

1. 

2. Tap the GRAPH button to draw parametric graph

   

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.

1. Press Calc button to open Calc panel:

   

2. Tap the Edit icon to enter the value of t

   

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

   x = ?
   y = ?
   dx/dt = ?
   dy/dt = ?
   dy/dx = ?

   

The TABLE panel: generate table of values

The Table panel allow you to generate a table of values.

1. Tap the Table button to open it:

   

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

   

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

   

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

   

Example

Example, Start=0.5 and Step=0.25

Tap Save to recalculate the table:

Settings the t range

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

1. Open the settings screen:

   

2. Select the Graph tab

   

3. Scroll to the Parametric graph section:

   

4. Change the Parametric start and Parametric stop with your value, tap OK to save

   

Example

Example:

x=sin(2t)+3sin(t)
y=2sin(3t)

• For the range of t from 0 to π

• For the range of t from −π to π