1.5.1—Trig graphs

For y=a sin(bx+c)+d, |a| is amplitude, period is 2π/|b|, −c/b is the horizontal shift, and d is the midline. Equivalent rules apply to cosine.

Mark the midline and one cycle before sketching. Check the sign of a and the requested domain; transformations change coordinates, not just the appearance.

y=2cos(3x−π)+1 has amplitude 2, period 2π/3, midline y=1 and shift π/3 to the right.

The coefficient inside the bracket changes period inversely; multiplying x by 3 does not stretch the graph by 3.