Icakubomfya ca inverse tangent (icaishibikwa na kabili nge cacubomfya ca arcus tangent) cipenda arctangent (atan) ya cipimo conse ica cine na umweo no kubwesheshapo akatundu ako tangent yako ilingana ne cipimo ico. Nga mulefwaya ukusanga akatundu ka cipelushi pa kwingisha ukunina no kubutuka ngo lubali ulupusana na ulupalamana, nelyo ukucincilamo bweseshe icipimo ca tangent ku madigirii nelyo amaradiana, ici cakusanga katundu cimipeela ifisangwamo bwangu-bwangu. Ingisheni idesimali nelyo icipimo ca kubali ukupusana / ukupalamana ukufuma ku katatu akalungama, saleni pakati ka madigirii na maradiana, elyo mukapokeele ifisangwamo ifya bwangu. Ici cacubomfya ca arc tan nacine cilecita ifishinte fya katatu ifyakusangwamo, icilecita ifimfuniko fya arctan(x), no kulanga itebulo lyonse lya tangent—fyonse ifilekabilwa mu masamu ya trigonometri, ukupenda, na ukupenda kwa navigation mu ncende imo.
Tangent ya Kubwesesha Icakupenda
Panuma ya kupenda konse, akatatu kalatuntulusha pakuti mumone ukuti θ = arctan(ukupusana / ukupalamana).
Ifimfuniko filalanga ico mwingisha pakuti mwingacincilamo icipimo ne katundu kako.
Inverse Tangent Cinshi?
Inverse tangent, ilembelwe ngo tan⁻¹(x), arctan(x), nelyo atan(x), ibwesesha akatundu ako tangent yako ilingana na x. Mu mabuku ya ku Europe na ya ku Germany ili shito lya musango umo lilemoneka ngo arcus tangens nelyo arkus tangens. Pa cintundu ca unit, arctan ibwesesha akatundu akalingana ne cipimo conse ca tangent ukwenda mu cintundu.
Mu katatu akalungama, tan(θ) = ukupusana / ukupalamana, kanshi arctan(ukupusana / ukupalamana) ipeela akatundu θ.
Ubupanda bwako ni mapinda yonse ayakwata umweo, ne ciputulwa cako ca mulandu cine (-π/2, π/2) nelyo (-90°, 90°).
Sunkeni icatelelwe pakumona ifyo ukwingisha konse ukwa cine ukutula akatundu pakati ka -90° na 90°.
Ifyo Mwinga Penda Inverse Tangent?
Bomfyeni θ = arctan(x) ilyo x ili icipimo ca desimali nelyo icipimo.
- Ishibeni icipimo x.
- Bomfyeni calculator ya masamu nelyo shito lya atan() pakupenda arctan(x).
- Cincilamukeni ifisangwamo nga mulefwaya amadigirii mu cifulo ca maradiana. Pindikisheni ifisangwamo fya maradiana pa 180/π pakupoka amadigirii, nelyo pindikisheni icipimo ca digirii pa π/180 pakucincilamo ku maradiana. Nangu fyonse fine, ifomula ya inverse tan ilatwalilila ukuba θ = arctan(x) lintu lyonse.
Lembeni icipimo pakutuntulusha intampulo shonse bwangu-bwangu.
Ifyo Mwinga Bomfya Iyi Inverse Tangent Calculator?
Saleni ukwingisha kwa desimali nelyo ukupusana/ukupalamana, saleni amadigirii nelyo amaradiana, elyo cineni Penda.
Inshila sha Kwingisha
Inshila ya desimali isumina ifipimo nge 0.5, 1, nelyo -2.75.
Inshila ya Ukupusana / Ukupalamana ilekanya pakubalilapo ukubali 2, elyo yabomfya arctan.
Icakutulapo cilalanga inshila ishalekana-lekana sha kwasuka pakubomfya bwangu.
Ifyo Mwinga Bomfya Inverse Tangent pa Calculator?
Cineni icitetekelo ca "2nd" nelyo "Shift" pa calculator ya masamu (nge Casio nelyo TI-84), elyo cineni aka "tan" pakufika pa tan⁻¹.
- Pilibusheni calculator elyo mubike inshila ya katundu ku madigirii (DEG) nelyo amaradiana (RAD).
- Cineni "2nd" nelyo "Shift." Ici citetekelo cilasansha imilimo iililembelwa pamulu ya citetekelo conse. Uku kusansha kwa shift tan ukufuma mu Casio, TI-84, na Sharp konse. Lyonse bikeni inshila yenu ya katundu pa DEG nelyo RAD ilyo mushilacine, pantu ukwingisha kumo kulebwesesha amapinda apusanapusana ukulingana ne nshila.
- Cineni icitetekelo ca "tan." Icilembesho cilalanga "tan⁻¹(" nelyo "atan(".
- Lembeni icipimo elyo mucine "=".
Icishinte pali onse pe samba lilangisha ifitetekelo ifyakucinwa pali calculator ya masamu ya TI-84.
Ukusanga tan⁻¹(1) = 45° pa calculator ya TI-84
Ifyo Mwinga Penda Inverse Tangent Ukwabula Calculator?
Bomfyeni ukukulisha kwa Taylor series kwa arctangent pakupendelamo arctan(x) ku minwe yenu: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... Uku kukulisha kwasangana ilyo |x| ≤ 1.
- Taylor Series (Maclaurin series). Icakubomfya ca arctangent series approximation cabomfya x − x³/3 + x⁵/5 − x⁷/7. Amashiwengwe ayengi yapeela ukulungama ukwakulu.
- Ifipimo fya Katundu Ifyaishibikwa. Ibukisheni ifisangwamo ifyacilamo bwingi: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- CORDIC Algorithm. Ino nshila ya pa mupaka wa hardware ipenda arctangent ukupitila mu kusungilila katundu ukwapitiwa.
Saleni amashiwengwe nga nshi ayakubikwapo. Moneni ifyo ukupendelamo kwakwata ululumbi ulwakulu.
Ifimfuniko fya Inverse Tangent
Ifimfuniko fya arctan(x) ni mukwafu ukukulilapo uwapangilwe ngo S uwapita mu ntendeko no kufika mupepi na ±π/2.
- Fyakwata ifyakulembwa fyakutambalala-pano mupepi na y = -π/2 na y = π/2.
- Fya mabilinganya, kanshi arctan(-x) = -arctan(x).
- Fyalatwalilila ukukula ukufuma ku kuso ku mwene na ku kulyo lyonse.
Koleni pamulu ya fimfuniko pakumona ifipimo ifyalungama.
Tebulo ya Tangent
Ifipimo fya tan inverse pa 0°, 30°, 45°, 60°, na 90° filemoneka mu masambililo yonse ya trigonometri kabili fyalikwata ubusuma bwa kufibukisha. Koleni umuselu onse wa tebulo pakwingisha ico cipimo ca standard mu calculator.
| x | arctan(x) Amadigirii | arctan(x) Amaradiana | Icipande ca π |
|---|---|---|---|
| −∞ | −90° | −1.5708 rad | −π/2 |
| −√3 ≈ −1.7321 | −60° | −1.0472 rad | −π/3 |
| −1 | −45° | −0.7854 rad | −π/4 |
| −1/√3 ≈ −0.5774 | −30° | −0.5236 rad | −π/6 |
| 0 | 0° | 0 rad | 0 |
| 1/√3 ≈ 0.5774 | 30° | 0.5236 rad | π/6 |
| 1 | 45° | 0.7854 rad | π/4 |
| √3 ≈ 1.7321 | 60° | 1.0472 rad | π/3 |
| +∞ | 90° | 1.5708 rad | π/2 |
Ifilembelo fya Inverse ya Tangent
Ifilembelo fya inverse ya tangent fyakwata inshila 3 isha standard: tan⁻¹(x), arctan(x), na atan(x).
- tan⁻¹(x) Iliilembelwa ilyashinga pa ma calculator.
- arctan(x) Iliilembelwa ilya standard mu masamu ayakulungama.
- atan(x) Icilembelo ca programming na software.
Abasambi bamo balamuita anti tangent mu nshila iyashilungama pantu ibwesesha fyo tangent yacita, lelo ici te cilembelo ca masamu icacindama.
Koleni icilembelo conse kumona uko cilemonekela mu masamu, pulogalamu, na ma calculator.
tan⁻¹(x) e cilembelo icaleshiwa bwino bwino pa ma calculator. Icipimikisho ca -1 cilelanga "umulimo wa inverse," te "1/tan(x)"
Ukusanga tan⁻¹ ya Mapinda Ayakana
Ili tan⁻¹ lya mapinda ayakana lyabwesesha akatundu akakana. Pantu arctangent ni shito lya mabilinganya, arctan(-x) = -arctan(x).
- arctan(-1) = -45° nelyo -π/4 amaradiana
- arctan(-√3) = -60° nelyo -π/3 amaradiana
Bushe tan⁻¹ lya -1 ni finshi?
Ili tan⁻¹ lya -1 ni -45° (-π/4 amaradiana nelyo -0.7854 amaradiana).
Ingisheni icipimo conse icakana kumona ifyo arctan ilapimba ukwingisha ukwakana ku katundu akakana.
Amepusho
Amasuko ku mepusho ayashinga pali inverse tangent.
Ee, tan⁻¹ ni icilembelo ica masamu ica standard pa inverse tangent, icishibikwa na kabili amba arctangent nelyo arctan. Icipendwa icakumulu ⁻¹ tashilependa 1/tan (ico ni cotangent). Mu kukanapo, tan⁻¹(x) ipusha ati: 'Nikatundu nshi akwata tangent iyalingana na x?' Icumwenako, tan⁻¹(1) = 45° pantu tan(45°) = 1. Kuti mwamona na kabili balilemba amba arctan(x) nelyo atan(x) mu ndimi sha mapulogalamu.
Icilangililo ca tangent cisenda akatundu elyo cacincilamo icipimo ca ulubali ulupusana ukulungenye ku lubali ulupalamana mu katatu akalungama. Inverse tangent (arctan) icita ukwabukene: isenda icipimo elyo yacincilamo akatundu akalingana. Icumwenako, tan(45°) = 1, kanshi arctan(1) = 45°. Tangent yakwata ubupanda bwa mapinda yonse ayakwata umweo ukushemo amapinda ayasalapulwa ayakushinina aya 90°, lelo inverse tangent isumina mapinda yonse ayakwata umweo no kutulapo amakatundu pakati ka −90° na 90° (−π/2 ukufika pa π/2 amaradiana).
Icitetekelo ca inverse tangent icala pamulu ya citetekelo ca tan pa ma calculator yonse ya masamu. Kuti mwafika kuli co, cineni icitetekelo ca 2nd nelyo Shift pakubalilapo, elyo cineni icitetekelo ca tan. Icilango cikalamonika tan⁻¹ nelyo arctan. Pa ma calculator ya graphing nge TI-84, cineni 2nd elyo cineni TAN. Pa ma calculator ya Casio, cineni SHIFT elyo cineni tan.
Bomfyeni ukukulisha kwa Taylor: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... pa |x| ≤ 1. Pa mapinda ayashilamo bwingi, ibukisheni amakatundu ayakumenyekana: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Kuti mwabomfya na kabili algorithm ya CORDIC. Pa mapinda aya panse ya [−1, 1], bomfyeni icishibilo arctan(x) = π/2 − arctan(1/x) pa x > 0.
Inverse tangent ya 1 ni 45° (nelyo π/4 amaradiana). Ici calingana pantu tan(45°) = 1. Mu katatu akalungama uko ulubali ulupusana na ulupalamana fyalilingana, akatundu ni 45°.
Tan icincilamo akatundu mu cipimo (ukupusana/ukupalamana), lelo inverse tan (arctan) icincilamo icipimo bweseshe ku katundu. Tan ya periodiki kabili kuti yatulapo umupinda onse uwakwata umweo, lelo arctan lyonse icincilamo akatundu akapusanapusana mu ciputulwa ca (−90°, 90°).
Ee, bomfyeni ifomula =ATAN(icishinka) mu Excel. Ici cilecincilamo ifisangwamo mu maradiana. Kuti mwacincilamo ku madigirii, bomfyeni =DEGREES(ATAN(icishinka)). Excel na yo yasumina =ATAN2(x, y) pa arctangent ya fyebo fibili.
Pilibusheni iPhone yenu ukuti ibe mu kumoneka mu kutambalala pakuti mwamone calculator ya masamu. Koleni aka 2nd kuti mwacincilamo ku milimo ya inverse. Icitetekelo ca tan cikacincilamo ukuba tan⁻¹. Ingisheni icishinka cenu elyo mukole tan⁻¹.
Mu katatu akalungama, inverse tangent ya cipimo ca ukupusana/ukupalamana yalingana na katundu pa kantu aka kene. Nga ukupusana = 3 na ukupalamana = 4, kanshi arctan(3/4) ≈ 36.87°.
Kuli ifyakucitako 6 ifyacilamo bwingi: (1) Ukufwaya inshila na GPS pa katundu ka kutungilila, (2) Ubukutonga pa katundu ka cipelushi, (3) Ifyakumoneka mu masamu ya maka, (4) Ifimfuniko fya kompyuta pa kupilibusha, (5) Ubukutonga bwa moto na amaka pa katundu ka mafasi, (6) Ifya muyayaya pa katundu ka kunyamuka.
Ukupitila mu tan(θ) = sin(θ)/cos(θ). Nga θ = arctan(x), kanshi sin(θ) = x/√(1+x²) na cos(θ) = 1/√(1+x²). Icipimwa ica derivative ca arctan(x) ni 1/(1+x²).
Ee. Icipimo ca cipelushi cilingana kumo ukupusana ukulungenye ku kupalamana mu katatu akalungama. Ingisheni ukunina kwenu ngo lubali ulupusana no kubutuka kwenu ngo lubali ulupalamana elyo icakubomfya cicincilamo akatundu ka kukosama mu madigirii na mu maradiana.
Ici cakubomfya cilipangwa ukulingana na arctangent. Nga mulefwaya calculator ya inverse trigonometry iyapwililila iya arcsin na arccos pamo na arctan, mulekabila icakubomfya icapwililila ici pyapene.