Základní velikost úhlu
Urči základní velikost úhlu:
\( \large -\Large \frac{{59\pi}}{5}\large \textrm{rad} \)
\( 59 : 10 = 6,… \)
\( k = 6 \)
\( {{\pi}}\left( {\frac{{59}}{5} − 6 · \frac{{10}}{5}} \right) = −\frac{11}{5}{{\pi}} \)
\( 2{{\pi}} − \frac{11}{5}{{\pi}} = \frac{{10}}{5}{{\pi}} − \frac{11}{5}{{\pi }} = −\frac{\pi}{5}\ \textrm{rad} \)
\( 59 : 10 = 4,… \)
\( k = 4 \)
\( {{\pi}}\left( {\frac{{59}}{5} − 4 · \frac{{10}}{5}} \right) = \frac{1}{5}{{\pi}} \)
\( 2{{\pi}} − \frac{1}{5}{{\pi}} = \frac{{10}}{5}{{\pi}} − \frac{1}{5}{{\pi }} = \frac{9\pi}{5}\ \textrm{rad} \)
\( 59 : 10 = 5,… \)
\( k = 5 \)
\( {{\pi}}\left( {\frac{{59}}{5} − 5 · \frac{{10}}{5}} \right) = −\frac{9}{5}{{\pi}} \)
\( 2{{\pi}} − \frac{9}{5}{{\pi}} = \frac{{10}}{5}{{\pi}} − \frac{9}{5}{{\pi }} = \frac{2\pi}{5}\ \textrm{rad} \)
\( 59 : 10 = 5,… \)
\( k = 5 \)
\( {{\pi}}\left( {\frac{{59}}{5} − 5 · \frac{{10}}{5}} \right) = −\frac{9}{5}{{\pi}} \)
\( 2{{\pi}} − \frac{9}{5}{{\pi}} = \frac{{10}}{5}{{\pi}} − \frac{9}{5}{{\pi }} = \frac{\pi}{5}\ \textrm{rad} \)