Dis inverse tangent kalkulieta, weh people call a arcus tangent kalkulieta too, work out di arctangent (atan) a any real number an give yuh di angle weh have dat tangent value. If yuh a find di angle a a slope, put inna di rise an di horizontal run as di opposite an adjacent side. If yuh just waan change a tangent ratio to degrees or radians, it give yuh di answer same time. Put inna a decimal or di ratio a di opposite / adjacent side from a right-angle triangle, den choose degrees or radians. Di tool draw a triangle weh yuh can interact wid, plot di arctan(x) graph, an show a full tangent table fi help wid trigonometry, calculus, an navigation.
Inverse Tangent Kalkulieta
Di Answer
Work Out Already arctan(1)
45°
Degrees 45°
Radians 0.7854 rad
Gradians 50 grad
Fraction a ฯ π/4
Right-Angle Triangle Yuh Can Try
Every time yuh work out a value, di triangle change fi show seh ฮธ = arctan(opposite / adjacent).
Di Inverse Tangent Graph
Di graph mark di value weh yuh put in, so yuh can compare di number wid di angle.
Wah Inverse Tangent Mean?
Inverse tangent, weh yuh write as tanโปยน(x), arctan(x), or atan(x), give yuh di angle weh have a tangent equal to x. Some European an German textbook call di same function arcus tangens or arkus tangens. Pon di unit circle, arctan give yuh di angle weh match di tangent value.
Inna right-angle triangle, tan(ฮธ) = opposite / adjacent, so arctan(opposite / adjacent) give yuh di angle ฮธ.
It accept all real number, an di principal range a (-ฯ/2, ฯ/2), or (-90ยฐ, 90ยฐ). Di end value dem nuh included.
Try It: Domain an Range a arctan(x)
Move di slider fi see how any real input give a angle between -90ยฐ an 90ยฐ.
How fi Work Out Inverse Tangent?
Use ฮธ = arctan(x) when x a decimal value or a ratio.
- Find di value a x.
- Use a scientific kalkulieta or di atan() function fi work out arctan(x).
- If yuh need degrees instead a radians, multiply di radian answer by 180/ฯ. Fi change degrees back to radians, multiply by ฯ/180. Di inverse tan formula stay ฮธ = arctan(x) either way.
Try It: Work It Out Step by Step
Type a value an each step wi update same time.
1Value Yuh Put In: x = 1
2arctan(1) = 0.7854 rad
3Change di Unit: 0.7854 × 180/π = 45°
How fi Use Dis Inverse Tangent Kalkulieta?
Choose a decimal or opposite/adjacent input, pick degrees or radians, den press Work Out.
Way fi Put Inna Value
1
Decimal Value
Decimal mode accept value like 0.5, 1, or -2.75.
2
Opposite Side / Side Beside di Angle
Opposite / Adjacent mode divide di 2 side dem first, den apply arctan.
Di answer panel show di result inna different form so yuh can use it quick.
How fi Use Inverse Tangent pon a Kalkulieta?
Press di โ2ndโ or โShiftโ key pon a scientific kalkulieta, like Casio or TI-84, den press โtanโ fi get tanโปยน.
- Turn on di kalkulieta an set di angle mode to degrees (DEG) or radians (RAD).
- Press โ2ndโ or โShiftโ fi turn on di extra function dem weh print above each button. Casio, TI-84, an Sharp model use dis kinda key combination. Set DEG or RAD first, because di same input give different number depending pon di mode.
- Press di โtanโ key. Di screen wi show โtanโปยน(โ or โatan(โ.
- Type di value an press โ=โ.
Picture Guide: Find tanโปยน pon a Kalkulieta
Di picture below show di button dem fi press pon a TI-84 scientific kalkulieta.
Find tanโปยน(1) = 45ยฐ pon a TI-84 kalkulieta
How fi Work Out Inverse Tangent widout a Kalkulieta?
Use di arctangent Taylor series fi get a approximate answer by hand: arctan(x) = x โ xยณ/3 + xโต/5 โ xโท/7 + โฆ Di series converge when |x| โค 1.
- Taylor Series (Maclaurin series). Di approximation tool use x โ xยณ/3 + xโต/5 โ xโท/7. More term generally bring di answer closer to di true value.
- Angle Value Weh Yuh Know. Learn di common answer dem: arctan(0) = 0ยฐ, arctan(1) = 45ยฐ, arctan(โ3) = 60ยฐ.
- Di CORDIC Algorithm. Dis hardware method work out arctangent by rotating angle over an over.
Try It: Approximation wid di Taylor Series
Choose how much term fi include. Watch how di approximate answer get closer to di true value.
Di Inverse Tangent Graph
Di arctan(x) graph a one S-shape curve weh go up, pass through di origin, an get closer an closer to ยฑฯ/2.
- It have horizontal asymptote at y = -ฯ/2 an y = ฯ/2.
- It a odd function, so arctan(-x) = -arctan(x).
- It always go up from left to right.
Try It: Di arctan(x) Graph
Move yuh pointer over di graph fi check di exact value dem.
Di Tangent Table
Di tan inverse value dem at 0ยฐ, 30ยฐ, 45ยฐ, 60ยฐ, an 90ยฐ turn up inna nearly every trigonometry course, so it good fi learn dem. Click any row inna di table fi load dat standard value inna di kalkulieta.
| x | arctan(x) Degrees | arctan(x) Radians | Fraction a ฯ |
|---|---|---|---|
| −∞ | −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 |
How fi Write Inverse Tangent
People use 3 standard form fi write inverse tangent: tanโปยน(x), arctan(x), an atan(x).
- tanโปยน(x) Yuh see dis pon nuff physical kalkulieta.
- arctan(x) Dis a di standard form inna formal maths.
- atan(x) Yuh see dis inna programming an software.
Some student call it anti tangent because it reverse wah tangent do, but dat nuh a standard maths name.
Try It: Compare di Way Dem fi Write It
Click each form fi see weh it turn up inna maths, programming, an kalkulieta.
tanโปยน(x) a di form yuh see most pon physical kalkulieta. Di small -1 up top mean โinverse functionโ; it nuh mean โ1 / tan(x)โ.
Find tanโปยน fi Negative Number Dem
Di tanโปยน a a negative number give a negative angle. Arctangent a odd function, so arctan(-x) = -arctan(x).
- arctan(-1) = -45ยฐ or -ฯ/4 radians
- arctan(-โ3) = -60ยฐ or -ฯ/3 radians
Wah di tanโปยน a -1?
Di tanโปยน a -1 a -45ยฐ (-ฯ/4 radians or -0.7854 radians).
Try It: Explore Negative Value Dem
Put inna any negative number fi see how arctan give a negative angle from it.
arctan(-1) = -45° = -π/4 rad
arctan(1) = 45ยฐ ↔ arctan(-1) = -45ยฐ
Question Dem Weh People Ask
Answer fi di common question dem bout inverse tangent.
Yes. tanโปยน a di standard maths way fi write inverse tangent, weh dem call arctangent or arctan too. Di small โปยน up top nuh mean 1/tan; dat a cotangent. tanโปยน(x) ask: 'Which angle have a tangent weh equal x?' Fi example, tanโปยน(1) = 45ยฐ because tan(45ยฐ) = 1. Inna programming language, yuh might see arctan(x) or atan(x).
Tangent tek a angle an give yuh di ratio a di opposite side to di adjacent side inna right-angle triangle. Inverse tangent (arctan) do it di other way round: it tek di ratio an give yuh di angle. Fi example, tan(45ยฐ) = 1, so arctan(1) = 45ยฐ. Tangent accept any real angle except odd multiple a 90ยฐ. Inverse tangent accept any real number an give angle between โ90ยฐ an 90ยฐ (โฯ/2 to ฯ/2 radians), widout di two end value dem.
Pon most scientific kalkulieta, di inverse tangent marking deh above di tan key. Press 2nd or Shift first, den press tan. Di screen wi show tanโปยน or arctan. Pon a TI-84, press 2nd den TAN. Pon a Casio, press SHIFT den tan.
Use di Taylor series: arctan(x) = x โ xยณ/3 + xโต/5 โ xโท/7 + ... when |x| โค 1. Learn di common angle dem: arctan(0) = 0ยฐ, arctan(1/โ3) = 30ยฐ, arctan(1) = 45ยฐ, an arctan(โ3) = 60ยฐ. Yuh can use di CORDIC algorithm too. Fi positive value outside [โ1, 1], use arctan(x) = ฯ/2 โ arctan(1/x).
Di inverse tangent a 1 a 45ยฐ (or ฯ/4 radians), because tan(45ยฐ) = 1. Inna right-angle triangle weh di opposite an adjacent side equal, di angle a 45ยฐ.
Tan change a angle into a ratio (opposite/adjacent). Inverse tan (arctan) change di ratio back into a angle. Tan repeat at regular interval an can give any real number. Arctan always give one angle inna di range (โ90ยฐ, 90ยฐ).
Yes. Use =ATAN(value) inna Excel. It give di answer inna radians. Fi get degrees, use =DEGREES(ATAN(value)). Excel have =ATAN2(x, y) too, fi arctangent wid two input.
Turn yuh iPhone sideways fi bring up di scientific kalkulieta. Tap 2nd fi switch to di inverse function dem. Di tan button wi change to tanโปยน. Put inna yuh value an tap tanโปยน.
Inna right-angle triangle, di inverse tangent a di ratio opposite/adjacent give di angle at dat corner. If opposite = 3 an adjacent = 4, den arctan(3/4) โ 36.87ยฐ.
People use it inna 6 common way: (1) navigation an GPS fi bearing angle, (2) engineering fi slope angle, (3) physics fi force vector, (4) computer graphics fi rotation, (5) electrical engineering fi phase angle, an (6) astronomy fi elevation angle.
Di connection a tan(ฮธ) = sin(ฮธ)/cos(ฮธ). If ฮธ = arctan(x), den sin(ฮธ) = x/โ(1+xยฒ) an cos(ฮธ) = 1/โ(1+xยฒ). Di derivative a arctan(x) a 1/(1+xยฒ).
Yes. Di slope ratio a di same as opposite divided by adjacent inna right-angle triangle. Put di rise inna di opposite-side box an di horizontal run inna di adjacent-side box. Di tool wi give di slope angle inna degrees an radians.
Dis tool build fi arctangent. If yuh need arcsin an arccos along wid arctan, yuh need a inverse trigonometry kalkulieta weh cover dem function deh too.