Trigonometric Function Graphs Math Example 1

Solution

1. 1
   Rewrite: $y=3\sin(2x-\pi)+1=3\sin\!\left(2\left(x-\frac{\pi}{2}\right)\right)+1$.
2. 2
   Read off parameters: $a=3$ (amplitude), $b=2$ (period $=2\pi/2=\pi$), $h=\pi/2$ (phase shift right $\pi/2$), $k=1$ (vertical shift up $1$).
3. 3
   Summary: oscillates between $k-|a|=1-3=-2$ and $k+|a|=1+3=4$, with period $\pi$, starting phase-shifted to the right by $\pi/2$.