cos' x + sin' x = 1 We can obtain similar (yet different) functions if we replace the unit circle with the "unit hyperbola" [C(x)]2 - [S(x)]2 = 1 Consider the following two functions C(x) = - ex 2 S(x) = 1) Prove that these functions satisfy the identity above them. Since these satisfy a hyperbolic equation we will call them the hyperbolic sine and hyperbolic cosine functions. Henceforth we will denote them -x cosh (x) = 2 sinh(x) = ex - 2 2) Find cosh(0) and sinh(0). 3) Determine whether cosh (x) and sinh(x) are odd, even or neither. The results in (1) and (2) above seem to mirror results we know for sine and cosine. However it turns out that the hyperbolic sine and the hyperbolic cosine are not periodic. 4) Solve the following two equations. (Hint: let z = e*) a) sinh(x) = 1 b) cosh(x) = 1 5) Explain why the answers to (4) prove that these functions are not periodic