Am trying to find the Fourier series coefficient ck for the following function

\begin{equation}

x\left(t\right)=\sin\left(wt+\theta \right)

\end{equation}

Here is my work

\begin{equation}

c_k=\frac{1}{T}\int_{-\frac{T}{2}}^{\frac{T}{2}}\:x\left(t\right)e^{-jkwt}dt

\end{equation}

Now x(t) can be written as

\begin{equation}

x\left(t\right)=\frac{\left(e^{j\left(wt+\theta \right)}-e^{-j\left(wt+\theta \:\right)}\right)}{2j}

\end{equation}

However:

\begin{equation}

c_k=\frac{1}{T}\int _{-\frac{T}{2}}^{\frac{T}{2}}\:\frac{\left(e^{j\left(wt+\theta \:\right)}-e^{-j\left(wt+\theta \:\:\right)}\right)}{2j}e^{-jkwt}dt

\end{equation}

would look very messy and am ending up with 2 sinc functions for my answer that I don't even know what do with. I can't put all the steps here but if somebody would steer me in the right direction I would really appreciate it.

# Electrical – Fourier series coefficient for sin(wt+theta)

fouriermath

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## Best Answer

Just pointers: