The exponentials $1, e^{2\pi ix}, \dots , e^{2\pi ikx}, \dots$ form the basis for trigonometric polynomials.
I know that from these we get $\cos{2\pi kx}$ and $\sin {2\pi kx}, k\in \mathbb{Z}$, but how can we get functions $\cos nx$ and $\sin nx$ from these?
I need this fact for the following proof from Stein and Shakarchi's Fourier Analysis.
