고장이 나서 sin, cos, tan, sin−1, cos−1, tan−1 버튼만 정상적으로 작동하는 계산기가 있다. 처음에 숫자창은 0이었다. 임의의 양의 유리수 q에 대해, 이 계산기의 버튼을 유한번 눌러서 q가 나타나도록 할 수 있음을 증명하여라. 단, 이 계산기는 오차 없이 무한 소숫점의 실수 계산을 한다고 가정하고, 모든 함수는 라디안으로 계산하는 것으로 한다.
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Severity: Warning
Message: mkdir(): Permission denied
Filename: libraries/Common.php
Line Number: 202
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: file_put_contents(/DATA/upload/polymath/latex/ec163044d23dff00b4db0727d1d19e4c.gif): failed to open stream: No such file or directory
Filename: libraries/Common.php
Line Number: 213
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once