Finding Symmetry

A semicircular ring of radius $R$ has a linear mass density $\lambda=\sin\theta$ , where $\theta$ is the angle made by the radius vector with the positive $X$ axis. Assuming the origin of the coordinate system to be at the circular center of the ring, find the coordinates of its center of mass.

• Assume $R= 1$ $m$
• If the coordinates can be expressed in the form of $(x,y)$ , find $x+y$ to three decimal places.
• Assume $X$ and $Y$ axes in the conventional directions.