Radian vs Degree
Degrees thiab radians yog units ntawm kev ntsuas angular. Ob qho tib si feem ntau siv hauv kev xyaum, hauv kev ua lej, physics, engineering, thiab ntau lwm yam kev tshawb fawb. Degree muaj keeb kwm khiav rov qab mus rau keeb kwm Babylonian thaum ub thaum radian yog lub tswv yim ua lej niaj hnub no tau qhia hauv 1714 los ntawm Roger Cotes.
Degree
Degree yog qhov feem ntau siv, chav tsev theem pib ntawm kev ntsuas angular. Txawm hais tias nws yog chav tsev ntau tshaj plaws hauv kev xyaum nws tsis yog SI chav ntsuas ntawm lub kaum ntse ntse.
A degree (arc degree) txhais tau tias yog 1/360th ntawm tag nrho lub kaum sab xis ntawm lub voj voog. Nws muab faib ua feeb (arc feeb) thiab vib nas this (arc vib nas this). Ib feeb arc yog 1/60th ntawm ib degree, thiab arc thib ob yog 1/60th ntawm arc feeb. Lwm txoj kev ntawm subdivision yog decimal degree, qhov twg arc degree muab faib ua 100. Ib puas ntawm ib degree yog paub thiab cim los ntawm lub sij hawm grad.
Radian
Ib radian txhais tau tias yog lub dav hlau lub kaum sab xis subtended los ntawm ib ncig arc ntawm qhov ntev uas yog sib npaug rau nws lub vojvoog.
Radian yog tus qauv ntsuas ntawm lub kaum ntse ntse, thiab nws tau siv ntau qhov kev ua lej thiab nws cov ntawv thov. Radian kuj yog ib qho muab tau los ntawm SI unit ntawm kev ntsuas angular, thiab nws tsis muaj qhov dav. Radians yog cim siv lub sij hawm rad qab tus lej qhov tseem ceeb.
Ib lub voj voog subtends ib lub kaum ntawm 2π rad ntawm qhov chaw thiab ib lub voj voog subtends π rad. Lub kaum sab xis yog π/2 rad.
Cov kev sib raug zoo no tso cai hloov pauv ntawm qib mus rau radians thiab rov ua dua.
1°=π/180 rad ↔ 1 rad=180°/π
Piv rau lwm chav tsev, radian nyiam vim nws qhov xwm txheej. Thaum ua ntawv thov, radian tso cai rau kev txhais lej ntau dua li lwm cov units. Tsuas yog nyob rau hauv cov tswv yim geometry, hauv kev suav lej, kev tsom xam, thiab lwm yam kev qhuab qhia ntawm lej radian yog siv.
Dab tsi yog qhov txawv ntawm Radians thiab Degrees?
• A degree yog ib chav tsev nkaus xwb raws li qhov kev sib hloov lossis tig thaum radian yog raws li qhov ntev arc tsim los ntawm txhua lub kaum sab xis.
• Ib degree yog 1/360th ntawm lub kaum sab xis ntawm lub voj voog thaum radian yog lub kaum sab xis subtended los ntawm ib ncig arc uas muaj tib ntev li nws lub vojvoog. Nws ua raws li lub voj voog subtends 3600 lossis 2π radians.
• Degrees muab faib ntxiv rau arc feeb thiab arc vib nas this, thaum radians tsis muaj kev faib, tab sis siv cov zauv rau cov kaum me me thiab cov kaum sab xis.
• Radian txhawb kev txhais cov ntsiab lus yooj yim hauv kev ua lej; Yog li ntawd, tso cai rau daim ntawv thov hauv physics thiab lwm yam kev tshawb fawb ntshiab (piv txwv li xav txog cov ntsiab lus ntawm tangential tshaj tawm).
• Ob degrees thiab radians yog qhov tsis muaj qhov ntsuas.
