Example Functions and Graphs
On this page you will find examples of interesting functions, along with their graphs created with the plotter tools on mathonthecloud.com!This page will be updated regularly! Visit our social media pages on Facebook and Twitter/X to see the newest examples!
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Explicit function examples
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Displaying 7 examples of the type: parametric
Multiple Function Types: A Bicycle Wheel
An offroad bike wheel represented with 3 functions! In the multi-type plotter, four types of functions are graphed simultaneously! This is useful when you want to visualize relationships and interactions between different types of equations.
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tags: explicit implicit polar parametric
Multiple Function Types: 3 Circles
Three ways to graph a circle! Standard form: `(x-a)^2+(y-b)^2=r^2`; Parametric form: `x=r*cos(t)+a, y=r*sin(t)+b`. 'a' and 'b' are x and y displacements, 'r' is the radius. In polar form, it is simply `r=radius` for a circle centered on the origin!
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tags: implicit polar parametric
Parametric Function: `x=cos(t)-(sin(t)^2)/(sqrt(2)), y=cos(t)*sin(t)`
The parametric function, `x=cos(t)-(sin(t)^2)/(sqrt(2)), y=cos(t)*sin(t)`, is known as the Fish Curve.
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tags: parametric
Parametric Function: `x=(1+tanh(10*sin(n*t))/10)*cos(t), y=(1+tanh(10*sin(n*t))/10)*sin(t)`
The parametric equations `x=(1+tanh(10*sin(n*t))/10)*cos(t), y=(1+tanh(10*sin(n*t))/10)*sin(t)` produces curves that are distinctly 'gear'-shaped, where 'n' is the number of teeth in the gear!
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tags: parametric
Parametric Function: `x=cos(cos(t))^2*(1+cos(1.92*t)^4), y=sin(sin(t))^2*sin(sin(1.92*t)^3)`
Parametric functions can produce fascinating images when they are graphed. Their complexity is only limited by the equations you create! Click this link to see an example!
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tags: parametric
Parametric Function: The Butterfly Curve
The Butterfly Curve is a set of parametric equations, `x=sin(t)*(E^(cos(t))-2cos(4t)-sin(t/12)^5); y=cos(t)*(E^(cos(t))-2cos(4t)-sin(t/12)^5)`, that looks like its namesake!
Go to the plotter page for this graph.⧉
tags: parametric
Parametric function: `x=t*cos(t); y=t*sin(t)`
Parametric functions can be used to produce many interesting graphs. A typical Archimedean spiral can be produced with the equations `x=t*cos(t); y=t*sin(t)`
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tags: parametric