How do you translate the graph of y=sin(x-pi/3) ?

Jul 25, 2018

Below

Explanation:

$y = \sin \left(x - \frac{\pi}{3}\right)$ is your $y = \sin x$ graph but shifted to the right by $\frac{\pi}{3}$ units

$y = a \sin \left(n x + b\right)$ is the general form
$a$ is the amplitude
$n$ is used to find the period of the function
$b$ is the shift to left or right

Therefore, wtih reference to the general form, y=sin(x-pi/3 has an amplitude of 1, a shift to the right by $\frac{\pi}{3}$ units.

The period is found using this equation
$T = \frac{2 \pi}{n}$
$T = \frac{2 \pi}{1}$
$T = 2 \pi$
That means the graph finishes one cycle in $2 \pi$

Below is $y = \sin x$

graph{sinx [-10, 10, -5, 5]}

Below is $y = \sin \left(x - \frac{\pi}{3}\right)$. Notice that it is exactly the graph $y = \sin x$ but moved to the right by $\frac{\pi}{3}$ units

graph{sin(x-pi/3) [-10, 10, -5, 5]}