i) Rechnen Sie in Grad ° (Winkelmaß) um!
- A)
, B) , C) , D) , E)![{\displaystyle 360\ rad}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f15ec1a9787270ad9d669ec13e89d25512971348)
ii) Rechnen Sie in Radiants (Bogenmaß) um
- A)
, B) , C) , D) , E)![{\displaystyle \ 145^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d952958d3dbde48fb6090a2380c4d8c2965bf0b4)
iii)Sind folgende Winkel mehr oder weniger als ein Halbkreis? Wo befinden sie sich im Einheitskreis?
- A)
, B) , C) , D) , E)![{\displaystyle \ 390^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/986a7034827b2e07729eed4b0feff026715023d5)
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daher
und ![{\displaystyle \quad 1rad={\frac {180^{\circ }}{\pi }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5841122f68daa7cd5c79aeba3dc8625393c639d7)
i)
- A)
![{\displaystyle \ 3\pi \ rad=3\pi \ {\frac {180^{\circ }}{\pi }}\ =540^{\circ },\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d52f6b000d4edce5b773a04065febfe0c45868)
- B)
![{\displaystyle \ {\frac {5\pi }{9}}\ rad={\frac {5\pi }{9}}\cdot {\frac {180^{\circ }}{\pi }}=100^{\circ },\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/4dca1226d3d597613a522650f81dfe59845525cc)
- C)
![{\displaystyle \ 0{,}2\ rad=0{,}2\cdot {\frac {180^{\circ }}{\pi }}\ ={\frac {36^{\circ }}{\pi }}\ \approx 11{,}5^{\circ },\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f32e11f2f5f3d3ca81c6a33e46a6367dc0b2709)
- 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 }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a703001a5cff9557c157524dd450a9fcb2e33fb0)
- E)
![{\displaystyle \ 360\ rad=360\cdot {\frac {180^{\circ }}{\pi }}\ ={\frac {64800^{\circ }}{\pi }}\ \approx 20626^{\circ }\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1e3ef153ed796b20489e96f35349c9a98b8f18c)
ii)
- A)
![{\displaystyle \ 300^{\circ }=300{\frac {\pi }{180}}\ rad\approx 5{,}24\ rad,\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ff8b3d9b9402fef4b4cf948ad2d928195629de0)
- B)
![{\displaystyle \ 0{,}2^{\circ }=0{,}2{\frac {\pi }{180}}\ rad\approx 0{,}0035\ rad,\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/10c5c2260b85508aea8caff4e460c3ed9fb6cfd6)
- C)
![{\displaystyle \ 3\pi ^{\circ }=3\pi {\frac {\pi }{180}}\ rad\approx 0{,}164\ rad,\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b2ce6fc1e27ab56e7a73979be79a72bd77665c9)
- D)
![{\displaystyle \ {\frac {170}{9\pi }}^{\circ }={\frac {170}{9\pi }}{\frac {\pi }{180}}\ rad=3400\ rad,\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b7db290a5aae4396887fb6a331de305459b579)
- E)
![{\displaystyle \ 145^{\circ }=145{\frac {\pi }{180}}\ rad\approx 2{,}53\ rad\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/4492a39b01dc268c8ce749173db74f7b30cbbb92)
iii) (Q für Quartil)
- A) 4.Q
B) 2.Q
C) 2.Q
D) 1.Q
E) 1.Q aber mehr als Halbkreis!