So I have a function $$f(t)\enspace\in\enspace L^{2}([0,1])$$ $$f(t)= \begin{cases}% \frac{1}{2} -t & \text{if $0 \leq t\leq \frac{1}{2},$}\\ 0 & \text{if $\frac{1}{2} \lt t\leq 1$} \end{cases}$$
How do I calculate the Fourier coefficients $$\left\langle{f|1} \right\rangle , \left\langle{f|A_{k} } \right\rangle , and \left\langle{f|B_{k}} \right\rangle$$
Any help is appreciated. Thanks.