Radiaan Radiaan (tähis rad ) on tasanurga mõõtühik SI-süsteemis. Raadiusepikkusele kaarele toetuv kesknurk on ühe radiaani suurune. Täisringis on 2 π {\displaystyle 2\pi }
2 π r a d = 360 ∘ . {\displaystyle 2\pi \,\mathrm {rad} =360^{\circ }.} Vastavalt
1 r a d = 360 ∘ 2 π = 180 ∘ π ≈ 57,295 77951 ∘ {\displaystyle 1\,\mathrm {rad} ={\frac {360^{\circ }}{2\pi }}={\frac {180^{\circ }}{\pi }}\approx 57{,}29577951^{\circ }} ehk
1 ∘ = 2 π 360 r a d = π 180 r a d ≈ 0,017 453293 r a d . {\displaystyle 1^{\circ }={\frac {2\pi }{360}}\,\mathrm {rad} ={\frac {\pi }{180}}\,\mathrm {rad} \approx 0{,}017453293\,\mathrm {rad} .} Radiaanid saab seega kraadideks ümber arvutada teguriga 180 ∘ π {\displaystyle {\frac {180^{\circ }}{\pi }}} π 180 ∘ . {\displaystyle {\frac {\pi }{180^{\circ }}}.}
Näiteid:
α = 3 2 π r a d = 3 2 π ⋅ 180 ∘ π = 3 2 ⋅ 180 ∘ = 270 ∘ . {\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 }.} β = 45 ∘ = 45 ∘ ⋅ π 180 ∘ = π 4 = π 4 r a d . {\displaystyle \beta =45^{\circ }=45^{\circ }\cdot {\frac {\pi }{\displaystyle 180^{\circ }}}={\frac {\pi }{4}}={\frac {\pi }{4}}\,\mathrm {rad} .}
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