Converting cosine to exponential form

I am trying to convert a cosine function to its exponential form but I do not know how to do it.

[more elaboration]

syms w y

function1 = input('user please enter input');

%user input is cos(y)

desired_output = (-1)^(w*pi) if y = w*pi

Answer 1

[Jan]

cos(x) = 0.5 * (exp(1i * x) + exp(-1i * x))

exp(ix) = cos(x) + 1i * sin(x)

I do not understand, why the desired output is (-1)^(w*pi).

[Andromeda]

(-1)^(w*pi) is merely arbitrary but it relates to stationery points of a curve. I am familiar with the forms of cosine and the exponential function that you have provided but that is not what I am looking for.

I am well aware that you can do the following but I want an alternative way of doing it

user_input = cos(3*y); %coefficient of y is 3

result = (-1)^(3*pi) %desired output