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Converting cosine to exponential form

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Andromeda
Andromeda 2021-11-7
编辑： Andromeda 2021-11-10
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

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回答（1 个）

Jan
Jan 2021-11-7
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).
  1 个评论
Andromeda
Andromeda 2021-11-7
编辑：Andromeda 2021-11-7
(-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

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