Question

Sketch a graph of the following function on paper.
f(x) = 2 sin(1/3x − π/3)

Find the zero(s) of f on the interval [0 + θ, T + θ), where T is the period and θ is the phase shift. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Answer 1

if you to sketch that graph
you need to find the period first
\[w=\frac{2\pi}{|B|}\]
if the function is \[f(x)=A\sin(Bx-C)\]

Answer 2

so in your case the period is \[w=\frac{2\pi}{1/3}=6\pi\]

Answer 3

so every 6 pi this function will repeat it self
we also need to know that sin is odd function (symmetrical with respect to the origin)

Answer 4

of course you need to find the zeros
then look for some points after than you can draw the graph

Answer 5

do you know how to find the zeros

Answer 6

?

Answer 7

No, I don't understand how to find zeroes @xapproachesinfinity

Answer 8

you have to set f(x)=0
meaning you need to solve \[2\sin(\frac{x}{3}-\frac{\pi}{3})=0 \Longrightarrow \sin(\frac{x}{3}-\frac{\pi}{3})=0\]