Use the sandwich theorem to explain why
Should I pick two other functions around this function and solve for their limits? What would be two good functions to pick?
Yes, pick two other functions. You want a function that is always greater than or equal to, and one that is always less than or equal to your function. Since cos(x) is always less than or equal to 1, the function x^2 is always greater than your function. I'll let you figure out the lower function.