Graphing Calculator | Polar Graphing Calculator | X-Intercepts

The world's most advanced Online Graphing Calculator, deploying the most sophisticated Cartesian and Polar coordinate system, with which you can animate polar and parametric graphs to see how they are traced, and graph with axes rotated too!

Advanced Online Graphing Calculator for function, equation (with variables on both sides) and parametric curve graphing. This intelligent graphing calculator automatically detects the type of expressions and graphs as you type using this syntax in the Cartesian or polar coordinate systems. This sophisticated online graphing calculator is the world's first and the only known graphing tool that lets you animate polar and parametric graphs to visualize how they are traced and constructed from start to end. Other easy-to-use features of this online graphing calculator allow you to find all the x-intercepts (zeros or roots of functions) on a bounded interval with a single click and label axes with π or any number. This function and parametric derivative calculator finds and also graphs derivatives. Full instruction

Interesting curves: Select an expression below to graph it using the Cartesian or polar coordinate system. For best results you may need to select Graph Fineness as "+1" or higher.

Functions

Lines

1 x+1 2x

Semi-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))
Functions – Polar

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)
Equations

Lines

y = 1 x = 1 y = x+1 x = y+1 3x + y = 2 3x - y +5 = 4x+2y-2

Circles

x^2+y^2 = 9 (x-2)^2 + (y-2)^2 = 4

Ellipses

x^2/4 + y^2/9 = 1 x^2-xy+2y^2-x-2y-8=0

Parabolas

y=x^2 y = x^2-4x+4 2x^2-4xy+2y^2-x-2y-2=0

Hyperbolas

x^2/4 - y^2/9 = 1 24x^2-50xy-49y^2+97x+93y-164=0

Other graphs

x^2 = y^2 sin(xy) = cos(xy)
Equations — Polar
Currently, not available.
Parametric

Lines

[t, 1] dom=(-5, 5) [1,t] dom=(-5, 5) [t, 2t] dom=(-5, 5)

Circles

[4sin(t), 4cos(t)] [3sin(t)+1, 3cos(t)+1]

Ellipses

[4cos(t), 3sin(t)] [3cos(t), 4sin(t)] [4sin(t), 3cos(t)] [3sin(t), 4cos(t)]

Parabolas

[t, t^2] dom=(-4, 4) [t^2, t] dom=(-4, 4)

Hyperbolas

[3sec(t), 4tan(t)] [3tan(t), 4sec(t)]

Other parametric graphs

[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]

Butterfly curve

[sin(t)(e^cos(t)-2cos(4t)-sin(t/12)^5), cos(t)(e^cos(t)-2cos(4t)-sin( t/12 )^5)] dom=(0, 12π)
Parametric – Polar

Lines

[2csc(t), t] [2sec(t), t] [1/(sin(t) - cos(t)), t]

Circles

[1, t] [2, t] [6sin(t), t] [8cos(t), t]

Spirals

[t, t] [t/5, t] dom=(0, 10π) [√(t), t] dom=(0, 10π) [1/t, t] dom=(0, 10π)

Roses

[4sin(3t), t] [4sin(2t), t] [4sin(5t), t] [4sin(4t), t]

Ellipses

[1/(1-.8cos(t)), t] [1/(1-.8sin(t)), t] [1/(1+.8cos(t)), t] [1/(1+.8sin(t)), t]

Parabolas

[1/(1-sin(t)), t] [1/(1+cos(t)), t] [1/(1+sin(t)), t] [1/(1-cos(t)), t]

Hyperbolas

[1/(1+2cos(t)), t] [4/(1+2sin(t)), t] [1/(1-2cos(t)), t] [4/(1-2sin(t)), t]

Cardioids

[3+3cos(t), t] [2+2sin(t), t] [3-3cos(t), t] [2-2sin(t), t]

Limacons

[2+3cos(t), t] [1+2sin(t), t] [2-3cos(t), t] [1-2sin(t), t]

Lemniscates

[√(4sin(2t)), t] [√(4cos(2t)), t]

Other parametric graphs

[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]