How many times in a day do the hour hand and the minute hand form a 90?
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If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times.
In a 24 hour day you get 2×22=44.
In a 24 hour day you get 2×22=44.
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