How can i find the parametric equations of a smiley face?

To create the parametric equations for a smiley face, you can break it down into components: the head (circle), eyes (circles), and mouth (arc). For the head, use the parameterization ( x = r \cos(t) ), ( y = r \sin(t) ) for ( t ) in ([0, 2\pi]), where ( r ) is the radius. For the eyes, you can use smaller circles at specific coordinates, e.g., ( x_{eye1} = -0.3, y_{eye1} = 0.5 ) and ( x_{eye2} = 0.3, y_{eye2} = 0.5) with small radii. The mouth can be represented with a semicircular arc using ( x = R \cos(t) ) and ( y = -R \sin(t) + b ) for ( t ) in ([0, \pi]).