What is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin bθ, what is an equation for the sine curve?
amplitude = 4, period = one-fourthpi, and a < 0.
The amplitude of the sine curve is given as 4, which means the maximum and minimum points on the curve are 4 units above and below the midline.
The period of the sine curve is given as one-fourth pi, which means one cycle of the curve occurs in a span of one-fourth of pi radians. The midline, or horizontal axis of the curve, is the x-axis.
Since a < 0, it indicates that the sine curve is reflected over the x-axis.
Therefore, the graph of one cycle of the sine curve will start at the midline, rise to a maximum point 4 units above the midline, go back to the midline, then go down to a minimum point 4 units below the midline, and finally return to the midline.
The equation for the sine curve is y = -4sin(8θ), where a = -4 and b = 8.