Some graphs with the Desmos free online graphing calculator, which can be found at https://www.desmos.com/. Desmos is also available as an iOS app and Android app.
Cosine Graphs in a Bottle
y= cos(2^x), cos(2^x), cos(2^x), cos(2^x)
y= cos(2^x), cos(2^x), cos(2^x), cos(2^x) 
red curve: x^3+y^4 = 6 sin(12*x^2)
blue curve: x^3+y^4 = 6 sin(12*x^2)
red: x^3+y^4 = 6 sin(12*x^2), blue: x^3+y^4 = 6 sin(12*x^2) 
A Spirograph
polar curve: r = 6 sin (2 sin (θ  2 (cos (θ^1.02)))
polar curve: r = 6 sin (2 sin (θ  2 (cos (θ^1.02))) 
y^2 = (8.65 * exp(x))/(3*x^0.2 3*x^2 + x^4)
y^2 = (8.65 * exp(x))/(3*x^0.2 3*x^2 + x^4) 
Double Teardrop Squeezed on One Side
right: x = 4.5(cos t + 1), y = 4 * sin t * sin (0.5*t^2)
left: x = 3 * (cos t  1), y = sin t * (0.5*t)^4
left: x = 3 * (cos t  1), y = sin t * (0.5*t)^4
4 π ≤ t ≤ 4 π
right: x = 4.5(cos t + 1), y = 4 * sin t * sin (0.5*t^2) left: x = 3 * (cos t  1), y = sin t * (0.5*t)^4 
Vibration
1.025*x*y^2 = 1.5*π*sin(x^3)
1.025*x*y^2 = 1.5*π*sin(x^3) 
x = 0.65*t + 1.5 sin(t^2)
y = 5 * (sin t)^3
4 π ≤ t ≤ 4 π
x = 0.65*t + 1.5 sin(t^2)
y = 5 * (sin t)^3

Get Desmos and have some fun!
Eddie
This blog is property of Edward Shore. 2015