# Syntax for Our Graphing Software

Our graphing software implemented by our graphing calculator is designed to be intelligent, intuitive, and user-friendly. To use it to its full potential, this guide provides more information on the syntax that should be used and conventions for entering functions and equations, parametric equations, and point sets.

## Syntax for Functions

To graph a function, for example, f(x) = `3x2+2x+1`, type in `3x^2+2x+1`

Or, when graphing in the polar coordinate system, if the expression is represented by r(θ) = `3θ2+2θ+1`, type in `3θ^2+2θ+1`

To type `θ` type `..t` (two dots followed by `t`). You can also use `x` for `θ`. All `x`'s are internally replaced by `θ` when graphing functions in polar coordinate system.

## Syntax for Equations

To graph an equation, for example, `x3-xy+2y2 = 5x+2y+5`, simply type in the equation (using the "=" sign). `x^3-xy+2y^2 = 5x+2y+5`

## Syntax for Parametric Curves

To graph a parametric curve represented, for example, by a function p(t) = [x(t), y(t)] = `[sin(t), cos(t)]` for `-π < t < π` or equivalently, by the equations x(t) = `sin(t)` y(t) = `cos(t)` `-π < t < π` type in [`sin(t),cos(t)`]   dom=(`-pi,pi`)

Or, when graphing in the polar coordinate system, if the expression is represented by p(t) = [r(t), θ(t)] = [`sin(t), cos(t)`]   for ```-π < t < π``` or equivalently, by the equations r(t) = `sin(t)` θ(t) = `cos(t)` `-π`` < t < π` type in [`sin(t), cos(t)`]   dom=(`-pi, pi`)

Note: Using [ ] to enclose `x(t),y(t)` or `r(t),θ(t)` is optional.

## Syntax for Points

To graph a set of points `{(xi,yi): i = 1,...,n}`, type in `x1, y1; x2, y2; ... xn, yn`

Or, when graphing the points `{(ri,θi): i = 1,...,n}` in the polar coordinate system, type in `r1, θ1; r2, θ2; ... rn, θn`

To make using our graphing software easier, we've implemented the following conventions.

When graphing functions and parametric curves, our software implemented in the Cartesian & polar graphing calculator graphs them on a domain (or interval) specified as `dom=(a, b)`. If you don't specify a domain, it will automatically append a suitable interval, which you can then adjust as desired.

For unspecified domains, the software will append `dom = (-∞, ∞)` or `dom = (0, 2π)` to function expressions, depending on whether it is graphing in the Cartesian or polar coordinate system, respectively. For parametric expressions, it will append `dom = (0, 2π)` for both Cartesian and polar graphing.

In polar or parametric graphing, the specified intervals must be bounded. If they are not, any instances of will be replaced by constant values.

Our graphing calculator recognizes `x`, `θ`, `t`, and `y` as variables and handles them intelligently. It automatically detects the type of expression as you type. For example, if you insert a comma, the labels on the relevant input panel will change to indicate that a parametric expression is being entered. If you delete the comma, the input panel will switch back to the function entering mode.

The calculator will then automatically replace:

• `t`'s and `θ`'s with `x`'s when graphing functions using the Cartesian coordinate system.
• `x`'s and `t`'s with `θ`'s when graphing functions using the polar coordinate system.
• `x`'s and `θ`'s with `t`'s when graphing parametric equations in both coordinate systems.

Remark: Although the variables `x`, `θ`, and `t` are intended to be used for functions (Cartesian/polar) and parametric curves, respectively, they can still be used interchangeably. For example, the function expression `xsin(t)` will be internally replaced by either `xsin(x)` or `θsin(θ)`, depending on the selected coordinate system. Similarly, the parametric expression `[xsin(t), θcos(x)]` will be replaced by `[tsin(t), tcos(t)]`. Clicking anywhere on the page will replace the variables in the input box with the appropriate ones.

Note: Unless the variable `y` is used in an equation, the software will treat it as either `x` or `θ`, depending on the selected coordinate system. In parametric expressions, any instances of the variable `y` will be replaced with a `t`.