Transform and reconstruct sine and cosine functions
The function is defined for all real x. Its range, extrema and phase-anchor pattern refer to this unrestricted function. Use the finite interval below only for key points and x-intercepts; the phase anchor may lie outside it
The function under consideration is
\[f(x)=\sin\left(\frac{1}{2}x\right)\]
Angles are measured in radians. The interval for key points and x-intercepts is \(\left[4\pi,8\pi\right]\)