In this paper, we study the superstablity problem of the cosine and sine type functional equations:
$$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$
and
$$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$
where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.