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Suppose I am looking for the following quantity: [itex]\sphericalangle[/itex] c

_{n}, where c

_{n}= [itex]\frac{sin(\frac{nπ}{2})}{nπ}[/itex]. c

_{n}is a complex number.

According to the book, "Signals and Systems" by Edward Kamen 2nd. Ed., [itex]\sphericalangle[/itex] c

_{n}= π for n = 3, 7, 11 ... , and c

_{n}= 0, for all other n.

The angle of a complex number is defined by arctan(b/a), where b is the imaginary component of the complex number, and a is the real component. In this case, there is no imaginary component (b).

Using the Euler Formula: e[itex]^{iθ}[/itex] = cos (θ) + jsin(θ), I can derive the relation of sin(θ) to an exponential, but I feel this is going backwards.

Any hints/insights is appreciated.