Karukureta yeArctangent

Inverse tangent ndiro basa rinodzosa kona ine tangent yakaenzana nenhamba yakapihwa. Inverse tangent yakanyorwa kuti tan⁻¹(x), arctan(x) kana atan(x), uye inodzosera tangent basa: tan(45°) = 1, saka tan⁻¹(1) = 45°.

Inverse tangent (arctangent) ndeimwe ye 6 inverse trigonometric mabasa mu trigonometry: arcsin, arccos, arctan, arccsc, arcsec uye arccot. Arctangent inogamuchira nhamba dzese chaidzo uye inodzosa kukosha kukuru pakati pe −90° ne 90° (−π/2 uye π/2 radians).

Mukona yekona yekurudyi, tangent yekona θ inoenzana nedivi rakapesana rakakamurwa nedivi riri pedyo. Iyo inverse tangent inotora reshiyo yakatarisana/yakatarisana yodzosa kona θ. Mu algebra, tan⁻¹ inogadzirisa equations senge tan θ = 2: θ = tan⁻¹(2) = 63.43°.

• Input: chero nhamba chaiyo, sereshiyo, muteremu kana desimali.
• Output: kona mumadhigirii kana maradians.
• Range: −90° < θ < 90°, kana −π/2 < θ < π/2.

Kuti uverenge inverse tangent, patsanura divi rakapesana nedivi riri pedyo woisa tan⁻¹ kune mhedzisiro. The inverse tangent kuverenga ine 3 nhanho:

1. Divide the opposite side by the next side: x = zvakapesana/padyo.
2. Nyorera the inverse tangent: θ = tan⁻¹(x), in radians.
3. Shandura kona kuita madhigirii, kana zvichidiwa: madhigirii = radians × 180/π.

Opposite = 3 and adjacent = 4 ipa x = 0.75. tan⁻¹(0.75) = 0.6435 rad = 36.87°. Iyo hypotenuse inotevera kubva kuPythagorean theorem: √(3² + 4²) = 5.

Mimwe mienzaniso miviri yakatenderedza tangent: tan⁻¹(0) = 0° uye tan⁻¹(1/3) = 18.43° (0.3218 rad).

Kuti ushandise iyi inverse tangent calculator, sarudza nzira yekuisa, nyora kukosha uye verenga kona. Kushandisa iyo tan-1 Calculator inotora 5 matanho:

1. Sarudza iyo inopinza: Decimal / x, Opp / Adj (yakatarisana / yakatarisana) kana Point (x, y).
2. Pinda kukosha: a decimal, chikamu chakaita se 3/4 kana kutaura kwakadai 1/√3.
3. Tora 1 ye 9 mayunitsi emhedzisiro, anosanganisira madhigirii, radians, magiradhi uye maminetsi kana masekonzi earc.
4. Seta kutenderedza: nhamba, gumi, zana, zviuru kana kusvika 15 nzvimbo dzedesimali kuti uwane kunyatsojeka.
5. Verenga kona, kukosha chaiko, nhanho-nhanho mhinduro uye dhayagiramu. Batidza Ratidza mavara kudoma mativi matatu.

Iyi arc tan karukureta inogadziridza zvawanikwa paunenge uchinyora. Poindi (x, y) mapindiro anoshandisa atan2(y, x), saka arctan karukureta inodzosa kona yakazara mune ese 4 maquadrants, kubva −180° kusvika 180°.

The inverse tangent formula is θ = tan⁻¹(divi rakatarisana nekona / divi riri pedyo nekona).

Fomula yacho inobva pachiyero che tangent chekona yekona yekurudyi, tan θ = zvakapesana / zviri pedyo. Kushandisa tan⁻¹ kumativi ose kunoparadzanisa kona θ. Kune 7 inoenderana inverse tangent mafomula:

• Coordinates: θ = atan2(y, x) for a point (x, y).
• Slope: θ = tan⁻¹(m), uko m = kusimuka / kumhanya.
• Complement: tan⁻¹(x) + tan⁻¹(1/x) = 90° for x > 0.
• Sum: tan⁻¹(a) + tan⁻¹(b) = tan⁻¹((a + b) / (1 − ab)) for ab < 1.
• Derivative (calculus, differentiation): d/dx tan⁻¹(x) = 1 / (1 + x²).
• Integral (kubatanidzwa): ∫ tan⁻¹(x) dx = x·tan⁻¹(x) − ½·ln(1 + x²) + C.
• Nhamba dzakaoma uye hyperbolic mabasa: tan⁻¹(z) = (i/2)·ln((i + z) / (i − z)) = −i·tanh⁻¹(iz).

Inverse tangent mumadigiri inopa kona pachikero kubva −90° ku 90°. Kushandura mhedziso yeradian kuita madhigirii, wedzera ne 180/π ( nezve 57.2958) Iyi radians kune madhigirii shanduko inoverengwa θ° = θ rad × 180/π.

Dhigirii rinopatsanurwa kuita madhigirii, maminetsi nemasekonzi (DMS). Dhigirii rimwe rine 60 maminetsi, uye miniti imwe ine 60 masekonzi: tan⁻¹(0.75) = 36.8699° = 36° 52′ 11.6″. Kwemasekonzi kusvika madhigirii, patsanura masekonzi ne 3,600.

Inverse tangent mumaradians inopa kona searc kureba payuniti denderedzwa, pakati −π/2 uye π/2 (−1.5708 ku 1.5708). Imwe radian ikona ine arc padenderedzwa yakaenzana neradius, uye kutendeuka kwakazara ndiko 2π radians (360°).

Kuti madhigirii ashandure madhigirii, wedzera madhigirii ne π/180. Pane 4 inverse tangent values mumaradians akakosha kuziva:

• tan⁻¹(1) = π/4 = 0.7854 rad
• tan⁻¹(√3) = π/3 = 1.0472 rad
• tan⁻¹(0.75) = 0.6435 rad
• tan⁻¹(1/3) = 0.3218 rad

MATLAB, Excel, Python uye mitauro yakawanda yepurogiramu inodzoka atan inoguma nema radians. MATLAB inoshandisa atand(x) kumadhigirii, uye Excel inoputira mhedzisiro mu DEGREES().

Kuti ushandise inverse tangent pane karukureta yesainzi, tinya SHIFT kana 2nd kiyi, dzvanya tan, isa nhamba uye wodzvanya zvakaenzana. Pane 4 matanho:

1. Set the angle mode: DEG for degrees kana RAD for radians.
2. Press SHIFT (Casio), 2nd (Texas Instruments) kana INV kusvika tan⁻¹.
3. Dzvanya tan kuvhura tan⁻¹( wonyora nhamba yacho.
4. Press = kuratidza kona.

On a Casio fx-82 kana fx-991, kutevedzana kwakakosha SHIFT, tan, 1, = returns 45 mune degree mode uye 0.7853981634 mune radian mode. A wrong angle mode ndiyo inonyanya kukanganisa kukanganisa: tan⁻¹(1) zvinoratidza 0.785 mu RAD mode pachinzvimbo che 45.

Windows Calculator uye iPhone Calculator shandisa reverse order: nyora nhamba yacho kutanga, wobva wadzvanya tan⁻¹.

Kuti uwane inverse tangent pa Android Calculator (Google Calculator), vhura makiyi esainzi, baya INV wobaya tan⁻¹. Maitiro acho ane 4 matanho:

1. Vhura Calculator wobaya museve wekuwedzera uri pamusoro pekiyi, kana kutendeudzira runhare parutivi.
2. Tap DEG kana RAD kusarudza madhigirii kana madhigirii.
3. Tap INV: sin, cos uye tan kuchinja ku sin⁻¹, cos⁻¹ uye tan⁻¹.
4. Tap tan⁻¹, nyora nhamba uye baya =. tan⁻¹(1) inoratidza 45.

Samsung Calculator inotevera kurongeka kwakafanana: vhura makiyi esainzi, baya Inv, wobva wabaya tan⁻¹.

Kuti uwane inverse tangent pa iPhone Calculator, chinja kumaitiro esainzi, nyora nhamba, baya 2nd uye baya tan⁻¹. Maitiro acho ane 4 matanho:

1. Vhura Calculator. PaIOS 18, baya chiratidzo chekuverenga uye sarudza Sainzi; paIOS 17 kana kumberi, shandura iPhone kudivi.
2. Tarisa iyo angle mode: Rad pachiratidziro zvinoreva radians, uye Rad/Deg makiyi anochinja modes.
3. Type nhamba, semuenzaniso 1.
4. Tap 2nd, then tan⁻¹. Chiratidziro chinoratidza 45.

iPhone Calculator inoshandisa tan⁻¹ kunhamba iri pachiratidziro, saka nhamba yacho inouya pekutanga.

Kuti uwane inverse tangent pa Windows Calculator, chinja kuenda kuScientific mode, nyora nhamba, vhura Trigonometry, sarudza 2nd wosarudza tan⁻¹. Maitiro acho ane 4 matanho:

1. Vhura Calculator, sarudza menyu (☰) uye sarudza Sainzi.
2. Sarudza bhatani rekona kusvika raratidza DEG, RAD kana GRAD.
3. Type nhamba, semuenzaniso 1.
4. Open Trigonometry, sarudza 2nd, wozosarudza tan⁻¹. Chiratidziro chinoratidza 45.

Mudimburiko we keyboard we tan⁻¹ mu Windows Calculator is Shift + T.

Kuti uverenge inverse tangent isina karukureta, shandisa 1 ye 3 nzira: special triangles, Taylor series kana mutemo wekona-diki.

1. Makona matatu ekurudyi ipai hunhu chaihwo. A 45-45-90 triangle inopa tan⁻¹(1) = 45°,uye a 30-60-90 triangle inopa tan⁻¹(1/√3) = 30° uye tan⁻¹(√3) = 60°.
2. The Taylor series tan⁻¹(x) = x − x³/3 + x⁵/5 − x⁷/7 + … anoshanda |x| ≤ 1. For |x| > 1, shandisa tan⁻¹(x) = π/2 − tan⁻¹(1/x) apo x > 0. Matemu mana anopa tan⁻¹(0.5) ≈ 0.5 − 0.041667 + 0.00625 − 0.001116 = 0.463467 rad, pedyo nechokwadi 0.463648 rad (26.565°).
3. The small-angle rule tan⁻¹(x) ≈ x radians inogara mukati 0.4% for |x| ≤ 0.1.

Macalculator nemachipisi emakombuta anoongorora arctangent ne CORDIC algorithm (Coordinate Rotation DIgital Computer). CORDIC inotenderedza vheji kuburikidza nemakona madiki akamisikidzwa ane mashifiti uye ekuwedzera chete.

Iyo inverse ye tangent ine 4 zvinozivikanwa: tan⁻¹(x), arctan(x), atan(x) uye arctg(x).

Iyo −1 mu tan⁻¹(x) inoisa inverse function, kwete exponent. tan⁻¹(x) inosiyana kubva ku (tan x)⁻¹ = 1/tan(x), izvo zvakaenzana cot(x). Arc prefix inobva paunit denderedzwa: arctan(x) ndiyo arc kureba, mumaradians, ayo tangent iri x.

The arctan(x) graph ndeye inowedzera S-yakaita curve kuburikidza nekwakabva iyo inokwira kubva kune maviri akatwasuka asymptotes, y = π/2 uye y = −π/2. Iyo inverse tangent graph ine 5 zvinhu zvakakosha:

• Domain: nhamba dzese chaidzo, (−∞, ∞).
• Range: (−π/2, π/2), kana (−90°, 90°).
• Symmetry: basa risinganzwisisike, symmetric nezvekwakabva.
• Slope: 1 at x = 0, kubva pane yakabva 1 / (1 + x²).
• Inflection point: (0, 0).

Iyo arctan girafu chiratidzo che tangent girafu pa (−π/2, π/2) pamhiri pemutsara y = x. Iyo dura uye huwandu hwemagirafu maviri anochinjanisa nzvimbo.

The inverse tangent table lists tan⁻¹(x) kune zvakajairika tsika dze x mumadhigirii nemaradians. Hunhu chaihwo hunobva kumakona akakosha 15°, 30°, 45°, 60° uye 75°.

Tafura ye tangent inomhanya neimwe nzira, kubva pakona kuenda kureshiyo: kuverenga tangent kunopa tan(30°) = 0.5774, tan(45°) = 1 uye tan(60°) = 1.7321. Huru dzemipumburu dzinosvika 90°: tan⁻¹(45) = 88.73° uye tan⁻¹(100) = 89.43°.

Sarudza mutsara wekutakura kukosha mu calculator. Shandisa mabhatani anotenderedza kushandura pakati pehuwandu, gumi, zana, zviuru uye kunyatsojeka.

Kuwana tan⁻¹ yenhamba dzisina kunaka, tsvaga tan⁻¹ yehukoshi hwakanaka uye isa minus sign pamberi: tan⁻¹(−x) = −tan⁻¹(x). Arctangent ibasa risinganzwisisike, saka yekupinza isina kunaka inogara ichipa kona pakati −90° uye 0°.

• tan⁻¹(−0.5) = −26.57°
• tan⁻¹(−√3) = −60°
• tan⁻¹(−2) = −63.43°

A negative principal value inonongedzera muquadrant IV. Wedzera 180° ye quadrant II angle, kana poindi iri kuruboshwe rwe y-axis: atan2(1, −1) = 135°.

Chii chinonzi tan−1 che −1?

The tan⁻¹ ye −1 ndizvo −45°, kana −π/4 radians (−0.7854 rad). tan(−45°) = −1,uye −45° iri mukati mechikamu chikuru che −90° ku 90°. On a 0° ku 360° chikero, nzira imwe chete 315°.