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The covariance matrix is given by $$C_{X,Y}=\begin{bmatrix}E(XX)& E(XY) \\ E(YX )& E(YY) \end{bmatrix}$$ This can be written as below: $$C_{X,Y}=\begin{bmatrix}E(R^2cos^2(\Theta) )& E(Rcos(\Theta)Rsin(\Theta)) \\ E(Rsin(\Theta)Rcos(\Theta) )& E(R^2sin^2(\Theta)) \end{bmatrix}$$ Since $R$ and $\Theta$ are independent the expectation will ...