OpenGL texture mapping question. A texture space with coordinates $(s,t)$ is mapped to the cylinder below:

$x=cos$

$Y=$

$Z=sin$

The surface is projected orthographically to $(x,Y).$

The following mapping is defined:

$(s,t)=(0,0)(,)=(0,0)$

$(s,t)=(1,0)(,)=(\frac{}{2},0)$

$(s,t)=(1,1)(,)=(\frac{}{3},\frac{}{3})$

Pixel order scanning is used. Find the mapping transformation from $(x,Y)$ to $(s,t).$