Khalkhuleitara ya inverse tangent, e gape e bidiwang khalkhuleitara ya arcus tangent, e bala arctangent (atan) ya palo nngwe le nngwe ya nnete mme e busetsa sekhutlo se tangent ya sone e lekanang le boleng joo. Fa o batla sekhutlo sa slope ka go tsenya rise le run jaaka lehlakore le le lebaganeng le lehlakore le le bapileng, kgotsa o fetolela karolelano ya tangent go dikgato kgotsa diradiane, sediriswa seno sa go bona sekhutlo se go naya karabo ka bonako. Tsenya desimale kgotsa karolelano ya lehlakore le le lebaganeng / le le bapileng mo khutlotharong ya sekhutlo se se siameng, tlhopha fa gare ga dikgato le diradiane, mme o bone diphetho ka bonako. Khalkhuleitara eno ya arc tan e dira gape setshwantsho se se dirisanang sa khutlotharo, e bontsha kgrafu ya arctan(x), mme e bontsha tafole e e feletseng ya tangent - sengwe le sengwe se se tlhokegang mo trigonometry, calculus, le dipalo tsa navigation mo lefelong le le lengwe.
Inverse Tangent Khalkhuleitara
Morago ga palo nngwe le nngwe, khutlotharo e a ntlafadiwa gore o bone gore theta = arctan(lehlakore le le lebaganeng / le le bapileng).
Kgrafu e tshwaya input ya ga jaana gore o kgone go bapisa palo le sekhutlo sa yone.
Inverse Tangent ke eng?
Inverse tangent, e e kwalwang e le tan^-1(x), arctan(x), kgotsa atan(x), e busetsa sekhutlo se tangent ya sone e lekanang le x. Mo dibukeng dingwe tsa Yuropa le Sejeremane, tiro eno e le nngwe e bonala e le arcus tangens kgotsa arkus tangens. Mo unit circle, arctan e busetsa sekhutlo se se tsamaisanang le boleng bongwe le bongwe jwa tangent mo sedikong.
Mo khutlotharong ya sekhutlo se se siameng, tan(theta) = lehlakore le le lebaganeng / le le bapileng, ka jalo arctan(lehlakore le le lebaganeng / le le bapileng) e naya sekhutlo theta.
Domain ya yone ke dipalo tsotlhe tsa nnete, mme principal range ya yone ke (-pi/2, pi/2) kgotsa (-90 degrees, 90 degrees).
Sutisa slider go bona gore input nngwe le nngwe ya nnete e fetolelwa jang go sekhutlo se se fa gare ga -90 degrees le 90 degrees.
O bala inverse tangent jang?
Dirisa theta = arctan(x) fa x e le boleng jwa desimale kgotsa karolelano.
- Tlhopha boleng jwa x.
- Dirisa khalkhuleitara ya saense kgotsa function ya atan() go bala arctan(x).
- Fetolela karabo fa o tlhoka dikgato go na le diradiane. Atisa karabo ya diradiane ka 180/pi go bona dikgato, kgotsa atisa boleng jwa dikgato ka pi/180 go boela mo diradianeng. Ka tsela nngwe le nngwe, formula ya inverse tan e nna theta = arctan(x).
Tlanya boleng gore kgato nngwe le nngwe e ntlafadiwe ka bonako.
O dirisa khalkhuleitara eno ya inverse tangent jang?
Tlhopha input ya desimale kgotsa ya lehlakore le le lebaganeng/le le bapileng, tlhopha dikgato kgotsa diradiane, mme o tobetse Bala.
Mekgwa ya go Tsenya
Mokgwa wa desimale o amogela boleng jo bo jaaka 0.5, 1, kgotsa -2.75.
Mokgwa wa Le le lebaganeng / Le le bapileng o arola mahlakore a mabedi pele, morago o dirisa arctan.
Phanele ya karabo e bontsha mefuta e le mmalwa ya dikarabo gore o e dirise ka bonako.
O Dirisa Inverse Tangent Jang mo Khalkhuleitareng?
Gatelela konopo ya "2nd" kgotsa "Shift" mo khalkhuleitareng ya saense, jaaka Casio kgotsa TI-84, mme morago o gatelele konopo ya "tan" go fitlhelela tan^-1.
- Bulela khalkhuleitara mme o rulaganye angle mode go dikgato (DEG) kgotsa diradiane (RAD).
- Gatelela "2nd" kgotsa "Shift." Konopo eno e dirisa ditshebetso tsa bobedi tse di kwadilweng fa godimo ga dikonopo. Motsoako wa Shift le tan o tlwaelegile mo dikaelong tsa Casio, TI-84, le Sharp. Rulaganya angle mode ya gago go DEG kgotsa RAD pele, ka gonne input e le nngwe e busetsa dipalo tse di farologaneng go ya ka mode.
- Gatelela konopo ya "tan". Pontsho e tla bontsha "tan^-1(" kgotsa "atan(".
- Tlanya boleng mme o gatelele "=".
Setshwantsho se se fa tlase se bontsha dikonopo tse o tshwanetseng go di gatelela mo khalkhuleitareng ya saense ya TI-84.
Go bona tan^-1(1) = 45 degrees mo khalkhuleitareng ya TI-84
O Bala Inverse Tangent Jang Ntle le Khalkhuleitara?
Dirisa arctangent Taylor series expansion go lekanyetsa arctan(x) ka seatla: arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... Series eno e converga fa |x| <= 1.
- Taylor Series (Maclaurin series). Sediriswa sa go lekanyetsa arctangent series se dirisa x - x^3/3 + x^5/5 - x^7/7. Mareo a mantsi a naya nepagalo e kgolwane.
- Boleng jwa Dikgutlo jo bo Itsegeng. Gopola diphetho tse di tlwaelegileng: arctan(0) = 0 degrees, arctan(1) = 45 degrees, arctan(sqrt(3)) = 60 degrees.
- CORDIC Algorithm. Mokgwa ono wa maemo a hardware o bala arctangent ka go potololetsa sekhutlo gangwe le gape.
Tlhopha gore go tsenngwe mareo a le makae. Leba gore kakanyo e atamela jang boleng jwa nnete.
Kgrafu ya Inverse Tangent
Kgrafu ya arctan(x) ke curve e e tlhatlogang e e bopegileng jaaka S, e feta mo origin mme e atamela +/-pi/2.
- E na le horizontal asymptotes kwa y = -pi/2 le y = pi/2.
- Ke odd function, ka jalo arctan(-x) = -arctan(x).
- E oketsega ka metlha go tswa molemeng go ya mojeng.
Tshwara mouse godimo ga kgrafu go sekaseka boleng jo bo nepagetseng.
Tafole ya Tangent
Boleng jwa tan inverse kwa 0 degrees, 30 degrees, 45 degrees, 60 degrees, le 90 degrees bo bonala mo dithutong tse dintsi tsa trigonometry mme bo botlhokwa go bo gopola. Tobetsa mola mongwe le mongwe wa tafole go tsenya boleng joo jo bo tlwaelegileng mo khalkhuleitareng.
| x | arctan(x) Dikgato | arctan(x) Diradiane | Karolo ya pi |
|---|---|---|---|
| −∞ | −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 |
Mokgwa wa go Kwala Inverse ya Tangent
Mokgwa wa go kwala inverse ya tangent o na le mefuta e meraro e e tlwaelegileng: tan^-1(x), arctan(x), le atan(x).
- tan^-1(x) E tlwaelegile mo dikhalkhuleitareng tsa mmele.
- arctan(x) Ke mokgwa wa semmuso mo dipalong.
- atan(x) Ke mokgwa o o dirisiwang mo programming le software.
Baithuti bangwe ba e bitsa anti tangent ka tsela e e seng ya semmuso ka gonne e busetsa morago se tangent e se dirang, le fa seno e se lereo la semmuso la dipalo.
Tobetsa mokgwa mongwe le mongwe go bontsha kwa o bonalang teng mo dipalong, programming, le dikhalkhuleitareng.
tan^-1(x) ke mokgwa o o tlwaelegileng thata mo dikhalkhuleitareng tsa mmele. Superscript -1 e kaya "inverse function," e seng "1 / tan(x)".
Go Bona tan^-1 ya Dipalo Tse di Negatif
tan^-1 ya dipalo tse di negatif e busetsa sekhutlo se se negatif. Ka gonne arctangent ke odd function, arctan(-x) = -arctan(x).
- arctan(-1) = -45 degrees kgotsa -pi/4 diradiane
- arctan(-sqrt(3)) = -60 degrees kgotsa -pi/3 diradiane
tan^-1 ya -1 ke eng?
tan^-1 ya -1 ke -45 degrees (-pi/4 diradiane kgotsa -0.7854 diradiane).
Tsenya palo nngwe le nngwe e e negatif go bona gore arctan e fetolela jang di-input tse di negatif go dikgutlo tse di negatif.
Dipotso Tse di Bodiwang Gantsi
Dikarabo tsa dipotso tse di tlwaelegileng ka inverse tangent.
Ee. tan^-1 ke mokgwa o o tlwaelegileng wa dipalo wa go kwala inverse tangent, e gape e bidiwang arctangent kgotsa arctan. Superscript -1 ga e reye 1/tan, e leng cotangent. Go na le moo, tan^-1(x) e botsa gore: ke sekhutlo sefe se tangent ya sone e lekanang le x? Sekai, tan^-1(1) = 45 degrees ka gonne tan(45 degrees) = 1. Mo dipuong tsa go porograma o ka e bona gape e kwadilwe e le arctan(x) kgotsa atan(x).
Tangent e tsaya sekhutlo mme e busetsa karolelano ya lehlakore le le lebaganeng go lehlakore le le bapileng mo khutlotharong ya sekhutlo se se siameng. Inverse tangent (arctan) e dira se se kgatlhanong: e tsaya karolelano mme e busetsa sekhutlo se se tsamaisanang le yone. Sekai, tan(45 degrees) = 1, ka jalo arctan(1) = 45 degrees. Tangent e na le domain ya dipalo tsa nnete tsotlhe ntle le multiples tse di odd tsa 90 degrees, fa inverse tangent yone e amogela dipalo tsa nnete tsotlhe mme e ntsha dikgutlo tse di fa gare ga -90 degrees le 90 degrees (-pi/2 go ya go pi/2 diradiane).
Mo dikhalkhuleitareng tse dintsi tsa saense, konopo ya inverse tangent e nna fa godimo ga konopo ya tan. Go e fitlhelela, gatelela pele 2nd kgotsa Shift, morago o gatelele konopo ya tan. Pontsho e tla bontsha tan^-1 kgotsa arctan. Mo dikhalkhuleitareng tsa kgrafu jaaka TI-84, gatelela 2nd mme o gatelele TAN. Mo dikhalkhuleitareng tsa Casio, gatelela SHIFT mme o gatelele tan.
Dirisa Taylor series expansion: arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... fa |x| <= 1. Mo boleng jo bo tlwaelegileng, gopola dikgutlo tsa botlhokwa: arctan(0) = 0 degrees, arctan(1/sqrt(3)) = 30 degrees, arctan(1) = 45 degrees, arctan(sqrt(3)) = 60 degrees. O ka dirisa gape CORDIC algorithm. Mo boleng jo bo kwa ntle ga [-1, 1], dirisa identity arctan(x) = pi/2 - arctan(1/x) fa x > 0.
Inverse tangent ya 1 ke 45 degrees, kgotsa pi/4 diradiane. Seno se direga ka gonne tan(45 degrees) = 1. Mo khutlotharong ya sekhutlo se se siameng e lehlakore le le lebaganeng le lehlakore le le bapileng di lekanang, sekhutlo ke 45 degrees.
Tan e fetola sekhutlo go nna karolelano ya lehlakore le le lebaganeng/le le bapileng, fa inverse tan (arctan) e fetola karolelano eo go boela mo sekhutlong. Tan e a ipheta mme e ka ntsha palo nngwe le nngwe ya nnete, fa arctan yone ka metlha e busetsa sekhutlo se le sengwe mo lefelong la (-90 degrees, 90 degrees).
Ee, dirisa formula =ATAN(value) mo Excel. Seno se busetsa karabo ka diradiane. Go e fetolela go dikgato, dirisa =DEGREES(ATAN(value)). Excel e tshegetsa gape =ATAN2(x, y) ya arctangent ya dikarolo tse pedi.
Phetola iPhone ya gago go nna landscape gore khalkhuleitara ya saense e bonale. Tobetsa konopo ya 2nd go fetela mo ditshebetsong tsa inverse. Konopo ya tan e tla fetoga tan^-1. Tsenya boleng jwa gago mme o tobetse tan^-1.
Mo khutlotharong ya sekhutlo se se siameng, inverse tangent ya karolelano ya lehlakore le le lebaganeng/le le bapileng e lekana le sekhutlo mo ntlha eo. Fa le le lebaganeng = 3 mme le le bapileng = 4, arctan(3/4) e ka nna 36.87 degrees.
Go na le ditiriso tse 6 tse di tlwaelegileng: (1) navigation le GPS ya dikgutlo tsa bearing, (2) boenjineri ya dikgutlo tsa slope, (3) fisikisi ya force vectors, (4) computer graphics ya rotation, (5) boenjineri jwa motlakase ya phase angles, (6) astronomy ya dikgutlo tsa elevation.
E amana ka tan(theta) = sin(theta)/cos(theta). Fa theta = arctan(x), jalo sin(theta) = x/sqrt(1+x^2) mme cos(theta) = 1/sqrt(1+x^2). Derivative ya arctan(x) ke 1/(1+x^2).
Ee. Karolelano ya slope e tshwana le lehlakore le le lebaganeng godimo ga le le bapileng mo khutlotharong ya sekhutlo se se siameng. Tsenya rise ya gago jaaka lehlakore le le lebaganeng le run ya gago jaaka lehlakore le le bapileng, mme sediriswa se tla busetsa sekhutlo sa incline ka dikgato le diradiane.
Sediriswa seno se agilwe segolobogolo bakeng sa arctangent. Fa o tlhoka khalkhuleitara e e feletseng ya inverse trigonometry e e akaretsang arcsin le arccos mmogo le arctan, o tla tlhoka sediriswa se se anameng thata sa inverse trigonometry.