We develop algorithms for multivariate integration and approximation in the weighted
half-period cosine space of smooth non-periodic functions. We use specially constructed
tent-transformed rank-1 lattice points as cubature nodes for integration and as sampling
points for approximation. For both integration and approximation, we study the connection
between the worst-case errors of our algorithms in the cosine space and the worst-case errors
of some related algorithms in the well-known weighted Korobov space of smooth periodic
functions. By exploiting this connection, we are able to obtain constructive worst-case error
bounds with good convergence rates for the cosine space.