Okakalkuleita ko inverse tangent (okati ka shiiwa yo kutya arcus tangent calculator) oha valula arctangent (atan) yomonhambala gwoshili nomoka oha alula engulo oyo tangent yayo ya faafana nomuwendo oo. Nge oto kongo engulo yoslope mokutula rise na run nga opposite na adjacent, ile oto lundulula tangent ratio ke degrees ile ke radians, oshilongitho shino oshi ku pe eshilipaleko shi fima. Tula decimal ile ratio yombinga opposite/adjacent yo right triangle, hoolola degrees ile radians, ndele to mono eshilipaleko sigo. Okakalkuleita koka ko arc tan oka li yo na omufaneko wo triangle ou ninge, graph ya arctan(x), netafula yotangent ya yela pamwe.
Inverse Tangent Kalkuleita
Eshilipaleko
Sha valulwa arctan(1)
45°
Degrees 45°
Radians 0.7854 rad
Gradians 50 grad
รโฌ Fraction π/4
Interactive Right Triangle
Konima yeshivalulo keshe, triangle oyi lunduluka opo u mone kutya ? = arctan(opposite / adjacent).
Graph yo Inverse Tangent
Graph oha ulike omuwendo wa hala nena opo u faafaneke omuwendo nengulo yayo.
Inverse tangent oshike?
Inverse tangent, yolekwa nga tan??(x), arctan(x), ile atan(x), oha alula engulo oyo tangent yayo ya faafana na x. Mombapila dombuto da Europe na Germany, oshilonga shino oshi shiiwa yo nga arcus tangens ile arkus tangens.
Mo right triangle, tan(?) = opposite / adjacent, ongaho arctan(opposite / adjacent) oha pe engulo ?.
Domain yayo oinombola aishe, ndele principal range oyo i li (-?/2, ?/2) ile (-90?, 90?).
Interactive: Domain na Range ya arctan(x)
Kudifa slider opo u mone omukalo omuwendo gwoshili u lundulukila ku engulo pokati ka -90? na 90?.
Inverse tangent oto valula ngahelipi?
Longitha ? = arctan(x) nge x i li decimal ile ratio.
- Konga omuwendo wa x.
- Longitha scientific calculator ile atan() function u valule arctan(x).
- Nge wa hala degrees ponhele ya radians, lundulula eshilipaleko. Hapunina result yaradian na 180/? u mone degrees, ile hapunina degree value na ?/180 u shune ko radians. Formula yi li yo ? = arctan(x).
Interactive: Step-by-Step Calculation
Nyola omuwendo opo etambo keshe li update sigo.
1Input: x = 1
2arctan(1) = 0.7854 rad
3Lundulula: 0.7854 × 180/π = 45°
Kalkuleita yeyi oto i longitha ngahelipi?
Hoolola decimal ile opposite/adjacent input, hoolola degrees ile radians, ndele to denge Valula.
Input Methods
1
Omuwendo wo Decimal
Decimal mode oha tambula omiwendo nga 0.5, 1, ile -2.75.
2
Opposite / Adjacent
Opposite/Adjacent mode otete wa topola ombinga mbali, konima opo to longitha arctan.
Result panel oha ulike omapala ga yooloka gopeshiwo opo u longithe sigo.
Inverse Tangent mokalkuleita oto i longitha ngahelipi?
Denga oshiboloto sha "2nd" ile "Shift" mokalkuleita yoscience (nga Casio ile TI-84), ndele konima denga "tan" u mone tan??.
- Yambeka kalkuleita ndele to set angle mode ku DEG ile RAD.
- Denga "2nd" ile "Shift". Oshi osha pendula secondary functions odo da nyolwa pombada yoshiboloto keshe.
- Denga oshiboloto sha "tan". Display oha ulike "tan??(" ile "atan(".
- Tula omuwendo ndele to denge "=".
Visual Guide: Okumona tan?? mokalkuleita
Omufaneko womezimo oha ulike omaboloto oo wa pumbwa oku denga ku TI-84 scientific calculator.
Okumona tan??(1) = 45? ku TI-84 calculator
Inverse Tangent oto i valula ngahelipi uhe na kalkuleita?
Longitha Taylor series expansion u landule arctan(x): arctan(x) = x ? x?/3 + x?/5 ? x?/7 + ... Oyo oha twa mo nge |x| ? 1.
- Taylor Series (Maclaurin). Oshilongitho shokufikama osha longitha x ? x?/3 + x?/5 ? x?/7. Omatumbo mahapu oha pe ondjokonona iwa.
- Known Angle Values. Dhimbuluka: arctan(0)=0?, arctan(1)=45?, arctan(?3)=60?.
- CORDIC Algorithm. Omukalo gomatokolo gocomputer/hardware oku valula arctangent moma rotation gangulo.
Interactive: Taylor Approximation
Hoolola omatumbo ngapi wa hala. Tala omukalo approximation i faafana neresult yoshili.
Graph yo Inverse Tangent
Graph ya arctan(x) i li curve ya S oyo i ya pombada, i pita momudingonoko (origin), ndele i endelela ku ??/2.
- Oi na horizontal asymptotes ku y = -?/2 na y = ?/2.
- Oi li odd function, ongaho arctan(-x) = -arctan(x).
- Oha yambuka alushe okufuma koxele okuya koxoome.
Interactive: Graph ya arctan(x)
Fikama pombada yograph opo u mone omiwendo yondjila.
Tafula yo Tangent
Omiwendo dotan inverse ku 0?, 30?, 45?, 60?, na 90? oda longithwa unene mo trigonometry. Denga row yo tafula opo omuwendo oo u longwe mokalkuleita.
| x | arctan(x) Degrees | arctan(x) Radians | รโฌ Fraction |
|---|---|---|---|
| −∞ | −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 |
Notation yinverse tangent
Notation yinverse tangent oi na omapala gatatu: tan??(x), arctan(x), na atan(x).
- tan??(x) Lahenya ku physical calculators.
- arctan(x) Notation yo standard mombalo yomesalo.
- atan(x) Notation yoku programming.
Vamwe ovanafunzi oha ifana anti tangent molwaashi oha alula oshilonga sha tangent, ndele etumbo eli kali standard yomesalo.
Interactive: Notation Comparison
Denga notation keshe opo u mone apa yi longithwa mo math, programming, na calculators.
tan??(x) oya longithwa unene mokalkuleita. Superscript -1 oya hala inverse function, hasho 1 / tan(x).
Oku mona tan?? yoomuwendo omibi
Tan?? yoomuwendo omibi oha alula engulo embi. Arctangent i li odd function: arctan(-x) = -arctan(x).
- arctan(-1) = -45? ile -?/4 radians
- arctan(-?3) = -60? ile -?/3 radians
Tan?? ya -1 oshike?
Tan?? ya -1 i li -45? (-?/4 radians ile -0.7854 radians).
Interactive: Negative Value Explorer
Tula omuwendo omubi keshe opo u mone omukalo arctan oha map omibi koomangulo omibi.
arctan(-1) = -45° = -π/4 rad
arctan(1) = 45? ↔ arctan(-1) = -45?
Omapulo ga ifo
Omayamukulo gomapulo ga ifo kombinga yinverse tangent.
Ee. Tanรขยยปรยน osho notation yomesalo yinverse tangent (arctan). Omuukwambo รขยยปรยน inau hala 1/tan; oha pula engulo ya na tangent = x.
Tangent oha kufa engulo nokupa ratio (opposite/adjacent). Inverse tangent oha kufa ratio nokupa engulo. Ngashi tan(45รยฐ)=1, ongaho arctan(1)=45รยฐ.
Pamahiku mahapu, shi li pombada yoshiboloto sha tan. Pula 2nd ile Shift tete, opo u ninge tanรขยยปรยน ile arctan.
Longitha Taylor series: arctan(x)=x รขหโ xรยณ/3 + xรขยยต/5 รขหโ xรขยยท/7 + ... molwa |x| รขโฐยค 1. Uta valula no values da tula: arctan(0), arctan(1), arctan(รขหลก3).
Arctan(1) = 45รยฐ (ile รโฌ/4 radians) molwa tan(45รยฐ)=1.
Tan oha lundulula engulo okuya ku ratio. Inverse tan oha lundulula ratio okuya ku engulo mo range (-90รยฐ, 90รยฐ).
Ee. Longitha =ATAN(value) (result mwaradians). Oku lundulula ku degrees, longitha =DEGREES(ATAN(value)).
Dimbulula iPhone landscape opo scientific calculator yi holoke. Denge 2nd; oshiboloto sha tan oshi ninga tanรขยยปรยน. Tula omuwendo ndele to denge tanรขยยปรยน.
Mo right triangle, arctan(opposite/adjacent) oha gave engulo yoshinyanghodo. Ngashi opposite=3, adjacent=4, engulo รขโฐห 36.87รยฐ.
Oshi longithwa mo navigation, engineering, physics, computer graphics, electrical phase angles, na astronomy.
Molwa tan(รยธ)=sin(รยธ)/cos(รยธ). Nge รยธ=arctan(x), ndele sin(รยธ)=x/รขหลก(1+xรยฒ) nosho yo cos(รยธ)=1/รขหลก(1+xรยฒ). Derivative yaarctan(x) yi li 1/(1+xรยฒ).
Ee. Slope ratio oya fa opposite/adjacent mo right triangle. Tula rise yoye nga opposite, run yoye nga adjacent; oshilongitho oshi ku pe engulo mu degrees nomwaradians.
Hasho. Oshino osha tungilwa arctan aike. Nge wa hala arcsin, arccos, naarctan pamwe, longitha full inverse trig calculator.