# ACF of $X_t = a + bt$

I was able to prove the following convergence results. But how can we determine the theoretical autocorrelation function of the deterministic sequence $$X_t = a + bt$$ and $$X_t = c\ \text{cos}(\omega t)$$? I think they should be 1 and $$\text{cos}(\omega h)$$, respectively. But I am not sure how to show it.