Calculate Phase Shift

New Numbers

Let φ=qπ{\color{orange}\varphi} = \color{red}q \cdot \pi an angle with 12π<φ<0\displaystyle -\frac{1}{2}\pi < {\color{orange}\varphi} < 0 and f\color{blue}f the function with f(x)=sin(14xφ)\displaystyle {\color{blue}f(x) = \sin \left(\frac{1}4 x-{\color{orange}\varphi}\right)} .

Determine q\color{red}q such that f(π)=1\displaystyle {\color{blue}f\left(\pi\right) = 1} .