A **polar function grapher** is a *function graphing calculator* that draws the graph of a function on a given *domain* in the polar coordinate system. Such a graph is called the **polar graph** or the **polar curve** of a given function.

The process of **graphing in the polar coordinate system** and rendering it by using a *function graphing calculator* is fundamentally *different* from graphing in the **Cartesian coordinate system**. This is due to the fact that a **polar graph** needs to be drawn progressively so that one can visualize how a **polar graph** is *constructed* on its domain.

This **function grapher**, deploying the most sophisticated **Cartesian & polar coordinate systems**, is the only known graphing tool that can graph in *non-perpendicular* **Cartesian coordinate system** and also properly helps visualize how a **polar curve** is progressively *constructed* by means of **polar graphing animation**. This way, you can watch how all your **cool polar graphs** are drawn step by step.

You can use this tremendously useful feature by pressing ► at the bottom of the **function graphing calculator** (if it's hidden, press the **Animate** button first).

It starts the animation of the **polar graphing process** of the **function** ** in focus**. The graph is drawn

*progressively*from the initial value θ₁ to the final value θ₂ of the

**radial axis**. The

**animated polar graph**shows the

*rotating*

**angular axes**(

**radial axes**) and the

**radial distances**.

You can then press **‖** to *pause* the **animation** or press **Done** to *stop* it. This also closes the animation interface. To display it again press the **Animate** button at the top of the polar grapher.

You can also change the **speed of ** **polar graphing animation** by using the **slider** provided

This free online **polar function graphing calculator** also draws **polar graphs** with the **polar axis** rotated.

**..t**is replaced by**θ**. (*You can also use x or t. They are internally replaced by θ*).**pi**is replaced by**π**.**inf**(**infinity**) is replaced by**∞**.

To graph **piecewise defined functions** type in each piece with the corresponding subinterval as a *single function*.

The quickest way to type **dom=(0, 2π)** or **dom=(-∞, ∞)** is by deleting the domain entirely, including **dom=**.

*You can use your mouse to*

**Rotate Axes**,**Translate**and**Change Scale**In addition to inputting data — by first pressing the *gear* button — you can use your mouse to perform some functionality unique to this **interactive function grapher** as outlined below.

- Click on (or near) an axis and move your mouse. That will
**rotate the axis**. The graph(s) are re-drawn in the*non-perpendicular***Cartesian coordinate system**or*generalized***polar coordinate system**. Click again to release the axis. - Drag the mouse to
**move the coordinate system**together with the graphs. - Double-click in the canvas to
**move the origin**to where was clicked. - Hold down Alt key and click on an axis to
**change the scale (zoom in one direction)**; the point which was clicked will be labelled "1" (or "-1") and becomes the new unit for that axis.

**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 pop-up menu.