Problem:
While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of for which the sine of degrees is the same as the sine of radians are and , where , and are positive integers. Find .
Solution:
Because radians is equivalent to degrees, the requested special values of satisfy . It follows from properties of the sine function that either
for some integers and . Thus either or , and the least positive values of are and , so .
The problems on this page are the property of the MAA's American Mathematics Competitions