# Between -2pi and 2pi, the graph of the equation y = sin x is symmetric with respect to what?

Not only in $\left[- 2 \pi , 2 \pi\right]$, but over the whole real set, we have that $\sin \left(- x\right) = - \sin \left(x\right)$. This means that, if you know the value of the sine in a point $x$, the opposite point with respect to the $y$-axis $- x$ will have an opposite value with respect to the $x$ axis, $- \sin \left(x\right)$.
Combining a symmetry with respect to $y$-axis and then $x$-axis, you get a syimmetry with respect to the origin.