Radiaan
Radiaan
Radiaan (tähis rad) on tasanurga mõõtühik SI-süsteemis. Raadiusepikkusele kaarele toetuv kesknurk on ühe radiaani suurune. Täisringis on
radiaani ehk 360 kraadi:
![{\displaystyle 2\pi \,\mathrm {rad} =360^{\circ }.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9994cabf917d51091ae3bcf00ee879e55f93ed)
Vastavalt
![{\displaystyle 1\,\mathrm {rad} ={\frac {360^{\circ }{2\pi }={\frac {180^{\circ }{\pi }\approx 57{,}29577951^{\circ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a54bc37713c0aaf34b9854b77fb6c87194a1cde4)
ehk
![{\displaystyle 1^{\circ }={\frac {2\pi }{360}\,\mathrm {rad} ={\frac {\pi }{180}\,\mathrm {rad} \approx 0{,}017453293\,\mathrm {rad} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e03d02559f007c7d8b537b50749b29222c6f4f9)
Radiaanid saab seega kraadideks ümber arvutada teguriga
ja kraadid radiaanideks teguriga
Näiteid:
![{\displaystyle \alpha ={\frac {3}{2}\,\pi \,\mathrm {rad} ={\frac {3}{2}\,\pi \cdot {\frac {180^{\circ }{\pi }={\frac {3}{2}\cdot 180^{\circ }=270^{\circ }.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ddbccb29e6cb47fdd78afb8f9224b65bc8c0c6e5)
![{\displaystyle \beta =45^{\circ }=45^{\circ }\cdot {\frac {\pi }{\displaystyle 180^{\circ }={\frac {\pi }{4}={\frac {\pi }{4}\,\mathrm {rad} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4161fb202ba58bcdc92c580c10eb9a462839972)
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