# Plottron/Eval GraphHelp and Information

Advanced 2D/3D Graphing and Scientific Calculator

General Help

## Notes

Some features described in this manual apply to Plottron only.

### General Notes

• The Minus key [−] is used for both subtraction and negation.
• Multiplication operator (*) can be omitted: before constants, before + after functions and parentheses.
2pisin(x)cos(x) = 2*pi*sin(x)*cos(x)
• Parentheses do not need to be matched.

1-2)(3+4 = (1-2)*(3+4)
(1-2(3+4 = 1-2*(3+4)

• Internally, all trigonometric function arguments are converted to radians. When working with complex numbers, Radian mode should be used.

### Internal Fractions

Numbers are stored internally as fractions when possible. There is no separate fraction button to enter fractions. Use the Divide key [÷] to enter fractions.

When internal fractions are enabled, points on graphs are evaluated using fractions. Always enable internal fractions for greater accuracy.

Numbers up to 6 decimal places are converted to fractions when internal fractions are enabled.

Does not apply to tables.

## Parameter Types

To change the parameter type: [MENU] → [Preferences] → [Parameter Type]
(Plottron only)

#### 2D Function

Yn is function of x.

Y1(x) = 2sin(x)cos(x)

#### 3D Function

Zn is function of x and y.

Z1(x,y) = x^2-y^2

#### 2D Parametric

XnT, YnT are functions of t.

X1T(t) = sin(t)
Y1T(t) = cos(t)

#### 3D Parametric

XnV, YnV, ZnV are functions of t, v.

X1V(t,v) = .02tsin(t)cos(v)
Y1V(t,v) = .02tsin(t)sin(v)
X1V(t,v) = .06v-4

#### 2D Polar

rn is a function of θ.

r1(θ) = sin(2θ)

## Function Editor

• By default, Plottron starts with the function editor.
• To enter functions into the list, select a function (e.g.: Y1 in 2D Function mode) by clicking or by using the [▲] and [▼] buttons, then use the editing buttons to edit the expression. The name of selected function is labelled in white.
• As functions are entered, they are stored as a user-defined function.
• To plot all of the defined functions:Press [MENU] on your device, then [Graph] in the resulting menu.

### Active Function

• When a function is selected to be edited in the function editor, it becomes the active function.
• The active function is used for the Information, Zero, Maximum, Minimum, and Intersect functions.
• In parametric modes, the entire relation for the active function is used for tracing.
• Click on the [=] button to toggle a function's visibility. The equals sign on a function (=) indicates that it is visible. When a function is invisible, it will not be graphed but can still be traced.
• In parametric modes, the equals sign only displays for the X function but it applies to the entire relation. Toggling the visibility of the X function is equivalent to toggling the visibility of the entire relation.
• In 3D parametric mode, the plot color can be selected for the entire relation by long pressing on the X function and choosing Set Color in the resulting dialog.
• To switch the active function in the graphing window, do one of the following:
• Press [↑]/[↓] directional pad buttons on device.
• Double-tap the screen in a calculation mode.
• Press [MENU] on your device, then [Set Active...] in resulting menu, then select the function in list that appears.
• Tap any coordinate in the upper left or right corners on screen.

### User-Defined Functions

As functions are entered in the function editor, they are stored as user-defined functions and can be accessed in both the function editor and the infix calculator by pressing [MENU] on device, then [User Functions] in the resulting menu.

#### Example:

The following functions plot a circle with a radius of 1 in 2D Function mode.
Y1(x) = √1-x²
Y2(x) = -Y1(x)

#### Warning:

Do not make functions refer to themselves or make them call each other:
Y1(x) = Y1(x)
Y1(x) = Y2(x), Y2(x) = Y1(x)
The application will quit due to stack overflow.

### Tables

• To display a table for a function, long press function and choose:
• Filled Table: a table filled with values according to the current Window settings.
• Table: enter in X, Y, T, V and/or θ coordinates in the appropriate text boxes and press the black Add Evaluation [+] button to evaluate the function at the coordinate(s).
• Expressions can be entered into the coordinate text boxes. For example, if π/3 is entered as a coordinate, the function is evaluated for π/3.
• If an error occurs, the dependent variable displays as NaN.
• To remove an evaluation: click on it, then press the black Remove Evaluation [−] button.

### Window

• To adjust the Window settings for the current parameter type: [MENU] → [Window] from the function editor.
• Click on the desired window parameter and use the editing keys to adjust it. The current window parameter is displayed in white.
• Expressions can be entered into the edit box. For example, if π/3 is entered into the edit box, the current window parameter is changed to ~1.0471975511965976.
• Expressions are evaluated as they are typed.
• Window settings are saved when the Window screen is closed.
• If an invalid window setting is entered, no error occurs and the setting is reset.
• If a Minimum parameter is greater than a Maximum parameter, the values are swapped.
• Resolutions (res) cannot exceed 10000.
• The Z offset setting is the distance from the camera to the graph.
• To reset the Window settings to their default values: [MENU] → [Reset].

## Graphing Window

The graphing window displays plots of all current functions according to the current Window setting. If an error occurs at a point of a function, it is not plotted and no error occurs.

### Modes

• Normal
• Touch and drag to rotate (3D) or scroll (2D) the graph.
• Volume +, − or double-tap to zoom in.
• Information, Zero, Extrema, Intersect
• Touch and drag to move the cursor on the graph.
• Volume +, − or double-tap to switch the active function.
• Enter value on keypad to move cursor on graph or to select boundary/limit.

The graphing window starts in Normal mode.

• Instead of touching and dragging, the buttons on the device's directional pad may be used.
• In a 2D mode, the up/down buttons switch the active function, while the left/right buttons move the cursor.
• In 3D Function mode, the buttons on the directional pad move the cursor in the X and Y dimensions.
• In 3D Parametric mode, the left/right buttons change variable t. and the up/down buttons change variable v.

• In a 2D mode, press [Value] to display keypad and input box. The [Zero] button changes to [OK].
• Full expressions can be entered into input box for evaluation.
• If an error occurs while evaluating expression, no error is displayed and 0 is used as input value.
• If current mode is Normal and [Value] is pressed, mode switches to Information.
• #### Different Modes

• In Information mode, type desired expression and press [OK] to move the cursor to the new value.
• In Zero/Extrema/Integrate modes, type expression and press [OK] to set lower boundary/limit. Then, type expression for upper boundary and press [OK] again to set upper boundary and use Zero/Maximum/Minimum/Integrate function.

### Calculation Functions

Calculation functions available in each mode
ModeTraceDerivativeOther*
2D Function
3D Function, Parametric
2D Parametric, Polar

*Zero, Maximum, Minimum, Intersect, Integrate

#### Information Mode

Traces the active function.

Press [Info] button to enter Information mode. The cursor's coordinates are displayed at the upper-left corner of the screen. Press [Info] again to return to Normal mode.

• In 2D Function and 2D Polar mode, the numerical derivative (dy/dx or dr/dθ) of the function at the cursor is also displayed.
• In 2D Parametric mode, the cursor moves with respect to variable t.
• In 3D Parametric mode, the cursor moves with respect to variables t (left/right) and v (up/down).
• In 2D Polar mode, the cursor moves with respect to variable θ.
• The cursor's coordinates are stored in the appropriate variables (x, y, z, t, and/or v). The derivative at the cursor (2D Function/2D Polar) is stored in variable m.

#### Zero

Finds a root (zero or x-intercept) of a function.

1. Press [Zero] to enter Zero mode. The [Zero] button will display [OK].
2. Move the cursor to the left of, and as close as possible, to the root. Press [OK].
3. Move the cursor to the right of, and as close as possible, to the root.
4. Press [OK] again.
The cursor moves to the root on the graph, and the coordinates are displayed at the upper-left corner of the screen. The mode changes to Normal. The coordinates of the zero are stored in variables x and y.

#### Maximum/Minimum

Finds local extrema on the graph.

1. Press [MENU] on device, then [Maximum] or [Minimum] in the menu to enter Extrema mode. The [Zero] button will display [OK].
2. Move the cursor to the left of, and as close as possible, to the extremum. Press [OK].
3. Move the cursor to the right of, and as close as possible, to the extremum.
4. Press [OK] again.
The cursor moves to the extremum on the graph, and the coordinates are displayed at the upper-left corner of the screen. The mode changes to Normal. The coordinates of the extremum are stored in variables x and y.

#### Intersect

Finds the coordinates of an intersection between two functions on the graph.

1. Press [MENU] on device, then [Intersect]. A list of functions appears.
2. Choose a function that intersects with the active function.
3. The cursor moves onto the active function. If necessary, change the active function. Move the cursor to the left of, and as close as possible, to the intersection. Press [OK].
4. The cursor moves onto the intersect function. If necessary, change this function using the D-pad or by double-tapping. Move the cursor to the right of, and as close as possible, to the intersection. Press [OK] again.
The cursor moves to the intersection on the graph, and the coordinates are displayed at the upper-left corner of the screen. The mode changes to Normal. The coordinates of the intersection are stored in variables x and y.

#### Integrate

Integrates a graph and shades the integrated area.

1. Press [MENU] on device, then [More], then [Integrate]. The [Zero] button will display [OK].
2. Move the cursor to the left bound. Press [OK].
3. Move the cursor to the right bound. Press [OK] again.
The integrated area is shaded. The left and right bounds and the integral are displayed at the upper-left corner of the screen. The mode changes to Normal. The integral is stored in the variable ans.

#### Parametric/Polar Derivatives (2D)

In 2D Parametric/Polar mode, press [MENU] on device, then [Derivative] in the resulting menu. A dialog is displayed displaying dy/dx, and dy/dt and dx/dt (parametric) or dr/dθ, dy/dθ, and dx/dθ (polar), calculated at the current cursor coordinates. Click on a derivative calculation to store it into variable m.

## Variables and Constants

See Variables and Constants in Infix Calculator Help.

## Preferences

### Graphing and Tables

 Angle Unit Adjusts measurement of angles. Applies to calculator, graphs, and tables. Degrees Radians Gradians Applies to standard trigonometric functions sine, cosine, tangent, arcsine, arccosine, arctangent. Snap to Increment In a calculation mode, restricts cursor movement to one increment as implied by the current window setting. RPN Calculator Use the RPN Calculator. Inertial Panning Accelerate panning and scrolling graphs. Parameter Type Changes the table and graphing parameters. See Parameter Types. 2D Function 3D Function 2D Parametric 3D Parametric 2D Polar Connect Plotted Points Whether to connect plotted points. In 3D modes, solid and wireframe modes are only enabled if this option is enabled. Show Axes Whether to show X, Y, and Z axes. Horizontal, Vertical Resolution Adjusts 3D Function graph resolution. Highest − Render 100 points High − 50 points Medium − 20 points Low − 10 points Note that if both resolutions are set to highest, 100 × 100 = 10000 points must be rendered. This may take a long time. Augmented Reality For 3D graphs, adjusts the camera based on the device position. Panning with the D-pad or touchscreen is disabled. When enabled, do not place device in strong magnetic fields. Lighting For 3D graphs, adds shading to show depth. This feature can be slow on some devices. If so, disable inertial panning. Smoothness Whether to smoothly shade 3D graph colors. White Background Whether to use a white or black background.

## Security

If the security dialog appears (Plottron), the application is unlicensed. Open Plottron with an internet connection once to license it. If this message persists, contact NIXON.