Translation of Sine and Cosine Graphs

y=a\cdot sin(bx+c)+d
y=a\cdot cos(bx+c)+d

y=sin(x)

amplitude=|a|\rightarrow amplitude=1
period=\frac{2\pi}{|b|}\rightarrow period=2\pi
phase\ shift=\frac{-c}{|b|}\rightarrow phase\ shift=0
vertical\ shift=d\rightarrow vertical\ shift=0
midline=y=d\rightarrow midline\ y=0

Example: y=(1sin(x+\frac{\pi}{2}))+1

a=1\rightarrow amp=|1|=1
b=1\rightarrow period=\frac{2\pi}{|1|}=2\pi
c=\frac{\pi}{2}\rightarrow phase=\frac{-\frac{\pi}{2}}{|1|}=-\frac{\pi}{2}
d=1\rightarrow vertical\ midline=1,\ y=1