Welcome to the world's most advanced **function grapher**. Utilizing the most sophisticated **Cartesian** and **polar** coordinate systems, this unique interactive online **function grapher** enables you graph functions in the **Cartesian coordinate system** (both **rectangular** and **oblique**—**non-orthogonal**). Additionally, it allows you to visualize functions in the **polar coordinate system**, and **animate** the process of **polar graphing** of functions with stunning clarity.

Our **function grapher** is unique in that it plots your function, say `f(x)`

, in the commonly used **Cartesian coordinate system**. Additionally, it allows you to visualize the **same** function in the **polar coordinate system**, where the variable `x`

represents the **angle** and `f(x)`

represents the **signed distance**. Since the common notation in the polar coordinate system uses `θ`

and `r`

, our grapher changes `f(x)`

to `r(θ)`

, without changing the defining function, enabling you to compare the function graph in **both** coordinate systems..

Our **function grapher** makes it easy to switch between **Cartesian graph** and **polar graph** of a given function. Simply, check or uncheck the **Polar checkbox**, to draw the function in the corresponding **coordinate system**.

This **polar function grapher** uses a unique **animation** algorithm to visualize the step-by-step construction of the graph of a function in the **polar coordinate system** like no other grapher. With its ability to **rotate radial axes**, it helps you understand the **polar graphing process for functions** in stunning animation.

## How Our Polar Graphs of Function Constructed

Our **polar function grapher** plots **graphs of functions** in the **polar coordinate system**, similarly to how you would graph them on paper, showing step-by-step construction using a sophisticated **animation** algorithm developed by A.M.I.R.

For each value of `θ`

, a temporary **radial axis** is drawn, making an angle of `θ`

with the **polar axis**. The **polar function graphing calculator** computes the signed distance `r(θ)`

and locates that point along the radial axis.

The **polar function grapher** then connects this point to the next point located using the same method with a slightly larger value of `θ`

. The online **polar function graphing calculator** thus completes the polar graph of the given function.

*Our polar grapher allows you to watch the entire animated graphing process, as detailed in Using Polar Graphing Animation Feature*.

**Lines**

**Semi-circles**

**Semi-ellipses**

**Parabolas**

**Semi-hyperbolas**

**Other graphs**

**Lines**

**Circles**

**Spirals**

**Roses**

**Ellipses**

**Parabolas**

**Hyperbolas**

**Cardioids**

**Limacons**

**Lemniscates**

**Butterfly curve**

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To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the context (pop-up) menu.

As you type:

**..t**is replaced by. (You can also use`θ`

`x`

or`t`

; they are internally replaced by`θ`

).**pi**is replaced by.`π`

**inf**(**infinity**) is replaced by.`∞`