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
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)
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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
θ. (You can also usexort; they are internally replaced byθ). - pi is replaced by
π. - inf (infinity) is replaced by
∞.
