Imibare ihindagurika (izwi kandi nka arcus tangent calculatrice) ibara arctan ubwitonzi (atan) bwumubare uwo ariwo wose kandi igasubiza inguni tangent ihwanye nagaciro. Waba urimo kubona inguni yumusozi winjira mukuzamuka no kwiruka nkibihabanye kandi byegeranye, cyangwa guhindura gusa igipimo gifatika kuri dogere cyangwa radiyo, iyi mfuruka iguha ibisubizo ako kanya. Injira icumi cyangwa igipimo cyimpande zinyuranye / zegeranye uhereye kuri mpandeshatu iburyo, hitamo hagati ya dogere na radiyo, hanyuma ubone ibisubizo ako kanya. Iyi arc tan calculatrice kandi ishushanya igishushanyo cya mpandeshatu, igashushanya igishushanyo arctan(x), kandi ikerekana imbonerahamwe yuzuye - ibintu byose bikenewe kuri trigonometrie, kubara, no kubara kugendagenda ahantu hamwe.
Tangent Kubara
Nyuma ya buri kubara, ivugurura rya mpandeshatu kugirango ubone ko θ = arctan (bitandukanye / byegeranye).
Igishushanyo cyerekana ibyinjijwe kugirango ubashe kugereranya umubare nu mfuruka.
Niki Kinyuranyo?
Inyuma ihindagurika, yanditswe nka tan⁻¹(x), arctan(x), cyangwa atan(x), isubiza inguni ingana na x. Mubitabo byu Burayi n’Ubudage iyi mikorere imwe igaragara nka arcus tangens cyangwa arkus tangens. Kuruziga rwibice, arctan asubiza inguni ihuye nigiciro icyo aricyo cyose gifatika.
Muri mpandeshatu iburyo, tan (θ) = ibinyuranye / byegeranye, bityo arctan (bitandukanye / byegeranye) bitanga inguni θ.
Indangarugero yacyo nimibare nyayo, kandi urwego nyamukuru ni (- π/2, π/2) cyangwa (-90 °, 90 °).
Himura igitambambuga kugirango urebe uko amakarita nyayo yinjiza kumurongo uri hagati ya -90 ° na 90 °.
Nigute Wabara Kubara Tangent?
Koresha θ = arctan(x) mugihe x ari agaciro ka cumi cyangwa igipimo.
- Menya agaciro x.
- Koresha ibara rya siyansi cyangwa imikorere ya atan() kubara arctan(x).
- Hindura ibisubizo niba ukeneye impamyabumenyi aho kuba radians. Kugwiza ibisubizo bya radian kuri 180 / π kugirango ubone impamyabumenyi, cyangwa ugwize agaciro ka dogere kuri π / 180 kugirango usubire kumurongo. Uko byagenda kose formulaire ihindagurika ikomeza θ = arctan(x) hose.
Andika agaciro kugirango uhindure buri ntambwe ako kanya.
Nigute ushobora gukoresha iyi calculatrice ya Tangent?
Hitamo icumi cyangwa ibinyuranye / byegeranye, hitamo impamyabumenyi cyangwa radiyo, hanyuma ukande Kubara.
Uburyo bwinjiza
Uburyo bwa cumi bwemera indangagaciro nka 0.5, 1, cyangwa -2.75.
Kurwanya / Guhuza uburyo bigabanya impande zombi mbere hanyuma bigashyirwa mu bikorwa arctan.
Igisubizo cyibisubizo byerekana uburyo bwinshi bwo gusubiza kugirango ukoreshwe vuba.
Nigute ushobora gukoresha Tangent ya Tangent kuri calculatrice?
Kanda urufunguzo rwa "2" cyangwa "Shift" kuri calculatrice ya siyansi (nka Casio cyangwa TI-84), hanyuma ukande buto "tan" kugirango ubone tan⁻¹.
- Fungura kuri calculatrice hanyuma ushireho inguni kuri dogere (DEG) cyangwa radians (RAD).
- Kanda “2” cyangwa “Shift.” Uru rufunguzo rutangiza imirimo ya kabiri yacapwe hejuru ya buri buto. Ihinduranya ryurufunguzo rwibanze ni rusange kuri Casio, TI-84, na Sharp. Buri gihe shyira inguni yawe kuri DEG cyangwa RAD mbere yo kuyikanda, kubera ko icyinjijwe kimwe gisubiza imibare itandukanye bitewe nuburyo.
- Kanda urufunguzo rwa "tan". Iyerekana ryerekana “tan⁻¹ (” cyangwa “atan (”.
- Andika agaciro hanyuma ukande "=".
Ishusho ikurikira irerekana buto nyayo yo gukanda kuri calculatrice ya TI-84.
Kubona tan⁻¹ (1) = 45 ° kuri calculatrice TI-84
Nigute ushobora Kubara Tangent Yinyuma idafite Kalkuliyeri?
Koresha arctan ubwitonzi bwa Taylor bwagutse kugirango ugereranye arctan(x) ukoresheje intoki: arctan(x) = x - x³ / 3 + x⁵ / 5 - x⁷ / 7 +… Uru rukurikirane ruhurira iyo |x| ≤ 1.
- Urutonde rwa Taylor (Urutonde rwa Maclaurin). arctan igikoresho cyoroheje cyo kugereranya igikoresho gikoresha x - x³ / 3 + x⁵ / 5 - x⁷ / 7. Amagambo menshi atanga ibisobanuro bihanitse.
- Indangagaciro zizwi. Fata mu mutwe ibisubizo rusange: arctan (0) = 0 °, arctan (1) = 45 °, arctan (√3) = 60 °.
- CORDIC Algorithm. Ubu buryo bwo murwego rwibikoresho bibara arctan byoroheje binyuze mu kuzenguruka inshuro nyinshi.
Hitamo umubare w'amagambo ugomba gushiramo. Reba uko ikigereranyo gihuza agaciro nyako.
Igishushanyo mbonera
Igishushanyo arctan(x) nigitekerezo cyiyongera S-umurongo uca mu nkomoko kandi wegera ± π/2.
- Ifite ibimenyetso simusiga kuri y = - π/2 na y = π/2.
- Ntibisanzwe, bityo arctan(-x) = -arctan(x).
- Burigihe bwiyongera kuva ibumoso ugana iburyo.
Hisha hejuru yishusho kugirango urebe agaciro nyako.
Imbonerahamwe
Agaciro keza kuri 0 °, 30 °, 45 °, 60 °, na 90 ° kugaragara mumasomo hafi ya yose ya trigonometrie kandi birakwiye kwiyemeza kwibuka. Kanda kumeza iyo ari yo yose kugirango ushireho agaciro gasanzwe muri calculatrice.
| x | arctan(x) Impamyabumenyi | arctan(x) Abanya Radiyani | Igice |
|---|---|---|---|
| −∞ | −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 |
Icyitonderwa kuri Inverse ya Tangent
Inyandiko yo guhinduranya tangent ifata uburyo 3 busanzwe: tan⁻¹(x), arctan(x), na atan(x).
- tan⁻¹(x) Bisanzwe kuri calculatrice yumubiri.
- arctan(x) Ibisanzwe mu mibare isanzwe.
- atan(x) Porogaramu na porogaramu.
Bamwe mubanyeshuri babyita anti tangent kuva ihindura ibyo tangent ikora, nubwo iyi atari imvugo isanzwe.
Kanda buri nyandiko kugirango ugaragaze aho igaragara mu mibare, gahunda, na calculatrice.
tan⁻¹(x) ni inyandiko isanzwe kuri calculatrice physique. Superscript -1 yerekana "imikorere ihindagurika," ntabwo "1 / tan (x)".
Kubona tan⁻¹ yimibare mibi
Tan⁻¹ yimibare mibi isubiza inguni mbi. Kuberako arctan ubwitonzi nigikorwa kidasanzwe, arctan(-x) = -arctan(x).
- arctan (- 1) = -45 ° cyangwa - π/4 imirasire
- arctan (- √3) = -60 ° cyangwa - π/3 radians
Tan⁻¹ ya -1 ni iki?
Tan⁻¹ ya -1 ni -45 ° (- π/4 imirasire cyangwa -0.7854 radians).
Shyiramo umubare mubi kugirango urebe uburyo arctan ikarita yinjiza nabi muburyo bubi.
Ibibazo
Ibisubizo kubibazo bisanzwe byerekeranye na tangent inverse.
Nibyo, tan⁻¹ ni imibare isanzwe yerekana imibare ihindagurika, nanone yitwa arctan witonda cyangwa arctan. Superscript ⁻¹ ntabwo isobanura 1 / tan (ni cotangent). Ahubwo, tan⁻¹(x) arabaza ati: 'Ni izihe mpande zifite tangent ingana na x?' Kurugero, tan⁻¹ (1) = 45 ° kuko tan (45 °) = 1. Urashobora kandi kubona yanditse nka arctan(x) cyangwa atan(x) mundimi za programme.
Imikorere ya tangent ifata inguni igasubiza ikigereranyo cyuruhande rutandukanye kuruhande rwegeranye muri mpandeshatu iburyo. Impinduka ihindagurika (arctan) ikora ibinyuranye: ifata igipimo igasubiza inguni ihuye. Kurugero, tan (45 °) = 1, bityo arctan (1) = 45 °. Tangent ifite urwego rwimibare nyayo usibye kugwiza bidasanzwe kwa 90 °, mugihe tangent ihindagurika yemera imibare nyayo kandi igasohoka inguni hagati ya −90 ° na 90 ° (- π/2 kugeza kuri π/2 radians).
Akabuto gahindagurika kicaye hejuru yurufunguzo kuri calculatrice ya siyanse. Kugirango uyigereho, kanda urufunguzo rwa 2 cyangwa Shift ubanza, hanyuma ukande buto ya tan. Iyerekana izerekana tan⁻¹ cyangwa arctan. Gufata ibara nka TI-84, kanda 2 hanyuma TAN. Kuri Casio kubara, kanda SHIFT hanyuma tan.
Koresha urutonde rwa Taylor kwagura: arctan(x) = x - x³ / 3 + x⁵ / 5 - x⁷ / 7 + ... kuri |x| ≤ 1. Ku ndangagaciro zisanzwe, fata mu mutwe inguni zingenzi: arctan (0) = 0 °, arctan (1 / √3) = 30 °, arctan (1) = 45 °, arctan ([7 Urashobora kandi gukoresha algorithm ya CORDIC. Ku ndangagaciro ziri hanze [−1, 1], koresha indangamuntu arctan(x) = π/2 - arctan (1 / x) kuri x> 0.
Impinduka zinyuranye za 1 ni 45 ° (cyangwa π/4 radians). Ni ukubera ko tan (45 °) = 1. Muri mpandeshatu iburyo aho impande zinyuranye kandi zegeranye zingana, inguni ni 45 °.
Igitereko gihindura inguni mu kigereranyo (gihabanye / cyegeranye), mugihe igitereko cyinyuma ([0]]) gihindura igipimo gisubira mu mfuruka. Tan ni igihe kandi irashobora gutanga umubare nyawo wose, mugihe arctan burigihe isubiza inguni idasanzwe murwego (−90 °, 90 °).
Nibyo, koresha formula =ATAN(value) muri Excel. Ibi bisubiza ibisubizo muri radians. Guhindura impamyabumenyi, koresha =DEGREES(ATAN(value)). Excel nayo ishyigikira = ATAN2(x, y) kubitekerezo bibiri arctan byoroheje.
Hindura iphone yawe kugirango yerekanwe icyerekezo kugirango ugaragaze kubara siyanse. Kanda buto ya 2 kugirango uhindure imikorere itandukanye. Akabuto ka tan kazahinduka kuri tan⁻¹. Injiza agaciro kawe hanyuma ukande tan⁻¹.
Muri mpandeshatu iburyo, tangent ihindagurika yikigereranyo gihabanye / yegeranye ingana inguni kuri iyo vertex. Niba bihabanye = 3 kandi byegeranye = 4, noneho arctan (3/4) ≈ 36.87 °.
Hano haribikorwa 6 bisanzwe:
Binyuze kuri tan(θ) = sin(θ)/cos(θ). Niba θ = arctan(x), noneho sin(θ) = x/√(1+x²) na cos(θ) = 1/√(1+x²). Inkomoko ya arctan(x) ni 1/(1+x²).
Yego. Ikigereranyo cyimisozi ni kimwe nikinyuranyo hejuru yegeranye na mpandeshatu iburyo. Injira kuzamuka kwawe nkuruhande rumwe no kwiruka kwawe nkuruhande rwegeranye kandi igikoresho gisubiza inguni ya mpinduramatwara muri dogere na radiyo.
Iki gikoresho cyubatswe byumwihariko kuri arctan witonda. Niba ukeneye imashini yuzuye ya trig calculatrice itwikiriye arcsin na arccos kuruhande arctan, uzakenera igikoresho kinini cya trigonometry.