How to read negative radians in the interval? Say a function's domain is $\{-\pi/2, \pi/2\}$. How should I interpret this interval?

It starts from where? To where? In what direction?

And if it starts from $3\pi/2$, would the next one be $-5\pi/3$.(because it starts from negative, $-\pi/2$).
 A: Usually an interval has parentheses, not braces.  Braces indicate a set of discrete values, while parentheses indicate an ordered pair or interval.  If the domain is $(-\frac \pi 2,\frac \pi 2)$, that is the interval of definition.  As an angle, $-\frac \pi 2$ radians is along the $-y$ axis or straight down on the paper.  $+\frac \pi 2$ radians is along the $+y$ axis or straight up on the paper.  For the last, it sounds like you are talking about special angles that are shown on the unit circle.  $\frac {3\pi}2$ is straight down, along $-y$.  Why would $-\frac {5\pi}3$ be next?  It depends on what angles you think are special.
A: The interval $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2} \right)$ is the right half of the unit circle. Negative angles rotate clockwise, so this means that $-\dfrac{\pi}{2}$ would rotate $\dfrac{\pi}{2}$ clockwise, ending up on the lower $y$-axis (or as you said, where $\dfrac{3\pi}{2}$ is located)
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You read the interval from left to right, meaning that this interval starts at $-\dfrac{\pi}{2}$ on the negative $y$-axis, and ends at $\dfrac{\pi}{2}$ on the positive $y$-axis (moving counterclockwise). 
