Use the even/odd properties of to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.
A) The Fourier Series will contain only cosine terms.
B) The Fourier Series will contain only sine terms.
C) The Fourier Series will contain both cosine and sine terms.

Question

Use the even/odd properties of  to predict (don't compute) whether the Fourier Series will contain only cosine terms, only sine terms or both.
A) The Fourier Series will contain only cosine terms. 
B) The Fourier Series will contain only sine terms. 
C) The Fourier Series will contain both cosine and sine terms.

Quizplus · Accepted Answer

The even/odd properties of the complex exponential function state that $e^{jx}$ is even, meaning that $e^{jx} = e^{-jx}$, if $x$ is a real number, and $e^{jx}$ is odd, meaning that $e^{jx} = -e^{-jx}$, if $x$ is an odd multiple of $\pi/2$. 
Looking at the given function $11eaa88b\_9106\_4940\_a696\_01562ef209b8\_TB5869\_11$, $11eaa88b$ is not a multiple of $\pi/2$, but $TB5869$ is an odd multiple of $\pi/2$. Therefore, we can use the odd property of $e^{jx}$ to conclude that the Fourier Series of the given function will contain both cosine and sine terms.

Use the Even/odd Properties of to Predict (Don't Compute)