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=.
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
1 x+1 2xSemi-circles
√(9-x^2) -√(9-x^2)Semi-ellipses
√(9-x^2/3) √(9-x^2/3)Parabolas
x^2 0.5x^2-4x+1 -(0.5x^2-4x+1)Semi-hyperbolas
√(x^2-4) -√(x^2-4)Other graphs
√(4sin(2x)) √(4cos(2x))Lines
2csc(θ) 2sec(θ) 1/(sin(θ) - cos(θ))Circles
1 2 6sin(θ) 8cos(θ)Spirals
θ θ/5 dom=(0, 10π) √(θ) dom=(0, 10π) 1/θ dom=(0, 10π)Roses
4sin(3θ) 4sin(2θ) 4sin(5θ) 4sin(4θ)Ellipses
1/(1-.8cos(θ)) 1/(1-.8sin(θ)) 1/(1+.8cos(θ)) 1/(1+.8sin(θ))Parabolas
1/(1-sin(θ)) 1/(1+cos(θ)) 1/(1+sin(θ)) 1/(1-cos(θ))Hyperbolas
1/(1+2cos(θ)) 4/(1+2sin(θ)) 1/(1-2cos(θ)) 4/(1-2sin(θ))Cardioids
3+3cos(θ) 2+2sin(θ) 3-3cos(θ) 2-2sin(θ)Limacons
2+3cos(θ) 1+2sin(θ) 2-3cos(θ) 1-2sin(θ)Lemniscates
√(4sin(2θ)) √(4cos(2θ))Butterfly curve
e^sin(θ)-2cos(4θ)+sin((2θ-π)/24)^5 dom=(0, 12π)
🔍+
1
🔍−
Calculator is loading.
Please wait....
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.