This worksheet plots the parametric curve known as "The Butterfly Curve" (see [url=http://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29]http://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29[/url]).[br][br]The equations defining [math]x[/math] and [math]y[/math] as functions of [math]t[/math] are [br][br][math]x\left(t\right)=\sin t\cdot\left(e^{\cos t}-2\cos4t-\sin^5\left(\frac{t}{12}\right)\right)[/math] and [math]y\left(t\right)=\cos t\cdot\left(e^{\cos t}-2\cos4t-\sin^5\left(\frac{t}{12}\right)\right)[/math].[br][br]The animation just plots the points [math]\left(x\left(t\right),y\left(t\right)\right)[/math] as [math]t[/math] takes values between -50 and 50. You can change the interval through which [math]t[/math] runs by changing the values of [math]a[/math] and [math]b[/math]. [br]