Question

Graph the function y=2sin(x-2pi/3). To draw the graph, plot all x-intercepts, minima and maxima within on period.

I need to graph at least 5 points. I have -pi, 0, pi, 2pi, 3pi, and 4pi along the x-axis

Answer 1

http://www.wolframalpha.com/input/?i=2sin%28x-2pi%2F3%29+domain+-pi..4pi

Answer 2

if \(x=-\pi\) then \(-\pi-\frac{2\pi}{3}=-\frac{5\pi}{3}\) and \(2\sin(-\frac{5\pi}{3})=2\times \frac{\sqrt{3}}{2}=\sqrt3\)

Answer 3

To graph x-intercepts, make y = 0
y = 2sin (x - 2Pi/3) = 0
sin (x - 2Pi/3) = 0 = sin 0 = 0 -> x = 2Pi/3
sin(x - 2Pi/3) = 0 = sin Pi -> x = Pi + 2Pi/3 = 5Pi/3
sin (x - 2Pi/3) = sin 2Pi -> x = 2pi + 2Pi/3 = 8Pi/3