# Plottron Help

## Hints and Examples

### Graphs

• To view 2D graphs, use the first parameter in the keypad (X, T, or θ)
• To view 3D graphs, use the second parameter in the keyp​ad (Y, V, or phi).
• Choose between different graph types by swiping left and choosing either Real or Complex.

#### Real graphs

• Regular
• To graph a parabola: `X^2`
• To graph ripples: `cos(1-X^2-Y^2)`
• Parametric
• To graph parametric relations, use the semicolon (;) operator to separate the different functions for X, Y, and Z.
• To graph a circle: `cos(T);sin(T)`
• To graph a cylinder: `cos(T);sin(T);V`
• Spherical
• To graph a spiral: `θ`
• To graph a sphere: `1+0φ`
• Implicit
Use equals (=) operator between two functions of X and/or Y.
• To graph a circle: `X^2+Y^2=10`
• To graph a crosshatch: `cos(X)=sin(Y)`
• To graph a hyperbola: `Y^2−X^2=1`

#### Visualization of complex functions

• Drawing
• Graphs, in green, the output of specified definition of function f : ℂ → ℂ on top of the drawn function input.
• Type `exp(Z)`. Draw vertical lines; they are mapped to circles. Draw horizontal lines; they are mapped to differently angled lines.
• Domain Coloring
• View domain coloring plots of the specified definition of function f : ℂ → ℂ, with each point in the complex plane associated with an HSV color with value 1.
• Type `Z` to view the identity color map.
• The argument of the complex number determines hue, and the magnitude of the complex number determines saturation.
• Complex argument in [0, 2π) → Hue angle in [0, 360°)
• Complex magnitude in [0, +∞) % 20 → Saturation in [0, 1)

### Calculator

• To set a variable, use the = operator.
• X=5
• Y=1+sin(pi)
• To use a variable, tap Rcl and choose a variable from the popover list. The list shows the variables and their values.
• To define a function, use either function variable f or g. Functions can take any number of arguments.
• f(X)=X+1
• g(X,Y)=1/(X^2+Y^2)
• Call a defined function like this:
• f(2)
• g(2,pi+1)
• To symbolically differentiate a function:
• D(X,sin(X)) → cos(X)
• D(Z,exp(Z)) → exp(Z)
• After calling this function, the value at the specified variable of the derivative is stored in variable ans.
• Swipe left for settings.
• Enable Speak in settings to speak buttons pressed and answers calculated, even if VoiceOver is off.

### General

• Brackets do not need to be matched.
• When using complex numbers, angle units are in radians regardless of the mode set in the settings.

### Known Issues

• The symbolic Taylor approximations for the factorial function ! are incorrect. Disable Symbolic Derivative to view Taylor approximations when using the factorial function.
• Do not create a self-referential function or a cycle of functions referring to each other, like:
• f(x)=f(x)
• f(x)=g(x) and g(x)=f(x)