i) Rechnen Sie in Grad ° (Winkelmaß) um! A)${\displaystyle \ 3\pi \ rad}$, B)${\displaystyle \ {\frac {5\pi }{9}}\ rad}$, C)${\displaystyle \ 0{,}2\ rad}$, D)${\displaystyle {\frac {5}{9\pi }}\ rad}$, E)${\displaystyle 360\ rad}$ ii) Rechnen Sie in Radiants (Bogenmaß) um A)${\displaystyle \ 300^{\circ }}$, B)${\displaystyle \ 0{,}2^{\circ }}$, C)${\displaystyle \ 3\pi ^{\circ }}$, D)${\displaystyle \ {\frac {170}{9\pi }}^{\circ }}$, E)${\displaystyle \ 145^{\circ }}$ iii)Sind folgende Winkel mehr oder weniger als ein Halbkreis?Wo befinden sie sich im Einheitskreis? A)${\displaystyle \ 300^{\circ }}$, B)${\displaystyle \ 100^{\circ }}$, C)${\displaystyle \ 2\ rad}$, D)${\displaystyle \ 1\ rad}$, E)${\displaystyle \ 390^{\circ }}$

${\displaystyle 360^{\circ }=2\pi \ rad\quad }$ daher
${\displaystyle \quad 1^{\circ }={\frac {\pi }{180}}\ rad\quad }$ und ${\displaystyle \quad 1rad={\frac {180^{\circ }}{\pi }}}$

i)

A)${\displaystyle \ 3\pi \ rad=3\pi \ {\frac {180^{\circ }}{\pi }}\ =540^{\circ },\quad }$
B)${\displaystyle \ {\frac {5\pi }{9}}\ rad={\frac {5\pi }{9}}\cdot {\frac {180^{\circ }}{\pi }}=100^{\circ },\quad }$
C)${\displaystyle \ 0{,}2\ rad=0{,}2\cdot {\frac {180^{\circ }}{\pi }}\ ={\frac {36^{\circ }}{\pi }}\ \approx 11{,}5^{\circ },\quad }$
D)${\displaystyle \ {\frac {5}{9\pi }}\ rad={\frac {5}{9\pi }}\cdot {\frac {180^{\circ }}{\pi }}={\frac {100^{\circ }}{\pi ^{2}}}\ \approx 10{,}1^{\circ },\quad }$
E)${\displaystyle \ 360\ rad=360\cdot {\frac {180^{\circ }}{\pi }}\ ={\frac {64800^{\circ }}{\pi }}\ \approx 20626^{\circ }\quad }$

ii)

A)${\displaystyle \ 300^{\circ }=300{\frac {\pi }{180}}\ rad\approx 5{,}24\ rad,\quad }$
B)${\displaystyle \ 0{,}2^{\circ }=0{,}2{\frac {\pi }{180}}\ rad\approx 0{,}0035\ rad,\quad }$
C)${\displaystyle \ 3\pi ^{\circ }=3\pi {\frac {\pi }{180}}\ rad\approx 0{,}164\ rad,\quad }$
D)${\displaystyle \ {\frac {170}{9\pi }}^{\circ }={\frac {170}{9\pi }}{\frac {\pi }{180}}\ rad=3400\ rad,\quad }$
E)${\displaystyle \ 145^{\circ }=145{\frac {\pi }{180}}\ rad\approx 2{,}53\ rad\quad }$

iii) (Q für Quartil)

A) 4.Q${\displaystyle \quad }$B) 2.Q${\displaystyle \quad }$C) 2.Q${\displaystyle \quad }$D) 1.Q${\displaystyle \quad }$E) 1.Q aber mehr als Halbkreis!