1. Let f(x) = cos(x). Recall that we define the inverse of cosine by restricting the domain of cosine to the interval [0, 7]. (a) The cosine function is periodic with period 27, so why don't we restrict the domain of f to the interval [0, 27]? (Explain by means of an example.) (b) When we restrict the sine function in order to define its inverse, we use the interval [- ?, ?]. Explain (through the use of an example) why we cannot use the same interval for defining the inverse of cosine. (c) Explain why we don't use the interval [0, "] for the restricted domain of cosine when defining the inverse of cosine. (d) Find an interval which does not contain 0 that we can use as a restricted domain for cosine in order to define its inverse. If g(x) = cos (x) is the inverse of cosine over this new restricted domain, then what is the value of g(1)