Marginal Probability Density Function of Stochastic Process

I was solving the following question and I derived the Auto correlation function and proved that it is a WSS process. However, I am not sure how to go about finding the Marginal probability density function. Should I find joint probability of a and b and then find marginal probability of each random variable?

Consider the stochastic process: x(t) = a sin(2πf0t) + b cos(2πf0t) where f0 is given, a and b are assumed to be Gaussian random variables, each having zero mean and unit standard deviation. • Is x(t) a wide sense stationary stochastic process? • Find the marginal density function and auto-correlation function of the random process x(t).