/sci/ - Science & Math

>>14887901
>>/sci/?task=search2&ghost=&search_text=&search_subject=putnam&search_username=&search_tripcode=&search_email=&search_filename=&search_datefrom=&search_dateto=&search_op=all&search_del=dontcare&search_int=dontcare&search_ord=new&search_capcode=all&search_res=post

>>11044434

A calculator is broken so that the only keys that still work are the [math] \, \sin, \; \cos, [/math] [math] \tan, \; \sin^{-1}, \; \cos^{-1}, \, [/math] and [math] \, \tan^{-1} \, [/math] buttons. The display initially shows 0. Given any positive rational number [math] \, q, \, [/math] show that pressing some finite sequence of buttons will yield [math] \, q [/math]. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.