A graphing calculator is a scientific calculator that is capable of graphing mathematical expressions, such as, functions in the Cartesian or polar coordinate systems.
In addition to functions, this graphing calculator, is capable of graphing equations (including implicitly defined functions), parametric equations and point sets in Cartesian or polar coordinate systems.
Syntax by Examples
- f(x) = x^2sin(x) + 2x + 1 (function)
- x^3-xy+2y^2 = 5x+2y+5 (equation)
- p(t) = [sin(t), cos(t)] (parametric)
- 1,2; -2, 2/3; sin(π/3), 2^3-1 (points)
In particular, you can use this graphing calculator to graph conic sections (in the standard and the general form ax^2 + bxy + cy^2 - dx + ey - f = 0, which can be a circle, ellipse, parabola, hyperbola or some degenerated graphs) and also graph level curves, which are in the form F(x,y) = c.
Unlike other graphing software, this graphing calculator can also graph in non-perpendicular (or non-orthogonal) Cartesian coordinate systems, where axes need not be horizontal or vertical and can intersect at any angle.
Another unique and tremendously useful feature of this polar graphing calculator is that it can animates polar graphs of functions. In addition, it is capable of animating the graph of parametric equations in both the Cartesian and polar coordinate systems. This way the Cartesian & polar graphing calculator shows how these type of graphs are constructed progressively from a starting value to an ending value on their specified domain (interval).
Furthermore, this graphing calculator can be used to solve equations in order to find x-intercepts (zeros or roots) of a given function.
Moreover, you can use the derivative graphing calculator to calculate derivatives of the 1st and 2nd order of a given function or parametric expression and graph their derivatives.
Note: to calculate the higher order derivatives and also partial derivatives of multi-variable functions you can use the partial derivative calculator.
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)Lines
y = 1 x = 1 y = x+1 x = y+1 3x + y = 2 3x - y +5 = 4x+2y-2Circles
x^2+y^2 = 9 (x-2)^2 + (y-2)^2 = 4Ellipses
x^2/4 + y^2/9 = 1 x^2-xy+2y^2-x-2y-8=0Parabolas
y=x^2 y = x^2-4x+4 2x^2-4xy+2y^2-x-2y-2=0Hyperbolas
x^2/4 - y^2/9 = 1 24x^2-50xy-49y^2+97x+93y-164=0Other graphs
x^2 = y^2 sin(xy) = cos(xy)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)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)]
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