I've been given the problem $S= \{\beta: -t + \beta_2\cos(t)+\beta_3\sin(t)\leq1, \text{ for all } t>0 \}$.
I was told that this set is the intersection of affine halfspaces, but I'm having trouble seeing this. How are these affine given the cos(t) and sin(t) terms?
What does this set look like? That is, how would I go about visualizing this set? I've been told to ignore the leading -t term and to try to describe the unit ball in $\mathbb{R}^2$ using tangent half spaces.