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By definition and with an authoritative reference, in which quadrant or quadrants does $90^\circ$ lie?

(There are non-authoritative references which answer the question, and a related question which touches on the topic, but I suppose I am asking if the the signs must be strictly positive/negative - with robust source(s) to back up the statement).

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    $\begingroup$ A completely analogous question seems, to me, to be "Is $0$ on the left or right half of the numberline?" $\endgroup$
    – pjs36
    Commented Jun 6, 2016 at 0:43
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    $\begingroup$ I doubt that there is an authoritative reference. In any context in which it matters an author should make clear what convention he or she is following. $\endgroup$ Commented Jun 6, 2016 at 0:44
  • $\begingroup$ @EthanBolker, if a statement by an authoritative source says something to that effect, then it is a perfectly acceptable answer. $\endgroup$
    – Damien
    Commented Jun 6, 2016 at 0:45
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    $\begingroup$ Directed angles in standard position (vertex at the origin with initial side on the positive $x$-axis) whose terminal side lies on one of the coordinates axes are called quadrantal angles. They do not lie in a quadrant since their terminal sides do not lie in a quadrant. $\endgroup$ Commented Jun 6, 2016 at 1:24
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    $\begingroup$ If you slice a cake into two pieces, which piece of cake has been cut? $\endgroup$
    – John Joy
    Commented Jun 6, 2016 at 12:31

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