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**IDontunderstand** y=d+sin(bx+c)

So if I have the equation:

sin(2x)=y; I know that the period will be pi. So the whole graph will occur between (0,0) and (pi,0)

Start at (0,0), Maximum (pi/4, 1); intercept at (pi/2, 0); Minimum (3Pi/4, -1); Intercept (pi,0)

Now if I have:

y=sin(x-(pi/4)) the graph gets shifted to the right pi/4 radians. So key points are

Start: (pi/4, 0); Maximum: (3pi/4, 1); Intercept: (5pi/4,0); minimum (7pi/4, -1); Complete (9pi/4,0)

If I put them together as Sin(2x-(pi/4)

Why does my horizontal shift get cut in half? Why does it not start at (pi/4)? Why does it start at (pi/8)? In my graphing calculator I see everything gets moved my (pi/8) when I have this equation.