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, $-\pi/2$).
2 Answers
$\begingroup$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) .
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).
$\endgroup$ $\begingroup$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.
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