1) This problem can be divided into 3 cases based on the range in which n lies and how trigonometric function varies within that range.3 cases are as follows:-
- ∀n,n∈[0, π/2 ], g(n)>f(n),and so f(n)=O(g(n))
- ∀n,n∈[π/2 , 3π/2 ],g(n)>f(n),and so f(n)=O(g(n))
- ∀n,n∈[π/2 , 3π/2 ],f(n)>g(n), and so f(n)= Ω(g(n))
And 1-3 will repeat for all subsequent values of sin and cos function as they are periodic in nature.So, from 1-3 we can observe that no specific relationship can be established between f(n) & g(n) as they behave differently in different ranges.
2)Same logic as 1