Graph one cycle of a sine function that has an amplitude of 3, has been reflected over the x axis, has period of pi/4, and a midline still y= -2.

Question

Write the equation of the sine function you graphed below

I know you can’t show graphs on here but can someone explain to me how I would graph this? I’m mostly stuck on the period part.

Answer 1

I find it best to "box in" the sine wave in order to draw it. First, draw the midline (y = -2) and the upper (y = 1) and lower bounds (y = -5).

Then vertical create the starting line - in this case there is no horizontal shift so the start is the y-axis. Then create the two "period" lines (where the period is completed. In this case the first is π/4 and the second is π/2:.

Split each box into 4 equal pieces and now just draw the sine wave in the box with the highs, lows, and midline crossings at the appropriate locations: