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
Consider the following transformed function:
\[f(x)=\sin\left(\frac{3}{2}x\right)\]
Angles are measured in radians. The interval for key points and x-intercepts is \(\left[\frac{4}{3}\pi,\frac{8}{3}\pi\right]\)