Question 1

What is the inverse tangent function?

Accepted Answer

The inverse tangent function, written as arctan(x) or tan⁻¹(x), is the inverse of the tangent function. It takes a ratio and returns the angle whose tangent is that ratio. The range of arctan is (-π/2, π/2) or (-90°, 90°), which means it always returns angles in the first and fourth quadrants.

Question 2

What is the difference between arctan and atan2?

Accepted Answer

arctan(x) takes one argument and returns angles between -π/2 and π/2. atan2(y,x) takes two arguments (y and x coordinates) and returns angles between -π and π, considering all four quadrants. Use arctan for simple ratios and atan2 when you need to determine the full angle in a coordinate system.

Question 3

What are the special values of inverse tangent?

Accepted Answer

Common special values include: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. These correspond to the standard angles in trigonometry. The calculator automatically recognizes these values and displays them in exact form (like π/4) when applicable.

Question 4

How do I convert between radians and degrees for inverse tangent?

Accepted Answer

To convert from radians to degrees, multiply by 180/π. To convert from degrees to radians, multiply by π/180. For example, arctan(1) = π/4 radians = 45°. Our calculator shows results in both units automatically, so you don't need to convert manually.

Question 5

Why is the range of arctan limited to (-π/2, π/2)?

Accepted Answer

The range is limited to make arctan a proper function (one output for each input). Since tangent is periodic and repeats every π radians, we choose the principal branch that includes angles from the first and fourth quadrants. This ensures that every real number input gives exactly one angle output.

Question 6

How is inverse tangent used in real applications?

Accepted Answer

Inverse tangent is used extensively in engineering, physics, and computer graphics for calculating angles from slopes or ratios. Common applications include finding angles in right triangles, determining directions in navigation, calculating phase angles in electrical engineering, and converting between Cartesian and polar coordinates.

Question 7

How do you use inverse tan on calculator?

Accepted Answer

To use inverse tan on calculator: 1) Enter your value, 2) Press the 'tan⁻¹' or 'arctan' button, 3) Get the result in radians or degrees. Our inverse tan calculator provides the same functionality as physical calculators but with step-by-step explanations and special value recognition for better understanding.

Question 8

What is the difference between arctan calculator and inverse tangent calculator?

Accepted Answer

Both arctan calculator and inverse tangent calculator refer to the same function - they calculate the inverse of the tangent function. 'Arctan' is the mathematical notation (arctangent), while 'inverse tangent' is the descriptive name. Our calculator supports both terms and provides the same accurate results regardless of which term you use.

Question 9

How do you calculate arctan of a value?

Accepted Answer

To calculate arctan of a value: 1) Identify the input value, 2) Use the arctan function: θ = arctan(x), 3) The result is the angle whose tangent equals the input value. Our arctan calculator handles this automatically and shows the step-by-step process, including special value recognition for common angles like 0°, 30°, 45°, and 60°.

Question 10

What does inverse tan of mean?

Accepted Answer

Inverse tan of means 'the angle whose tangent is' a given value. For example, 'inverse tan of 1' means 'the angle whose tangent is 1', which equals 45° or π/4 radians. Our calculator shows both the mathematical notation (arctan) and the descriptive meaning, making it easy to understand the relationship between the input and output.

Question 11

How do you find reverse tangent?

Accepted Answer

Reverse tangent is another term for inverse tangent or arctangent. To find reverse tangent: 1) Start with a ratio (opposite/adjacent), 2) Use arctan to find the angle, 3) Convert to desired units (degrees or radians). Our reverse tangent calculator provides this calculation with detailed explanations and special value recognition.

Question 12

What is tan-1 calculator used for?

Accepted Answer

A tan-1 calculator (also written as tan⁻¹) is used to find the angle when you know the tangent ratio. It's the inverse operation of the tangent function. Our tan-1 calculator handles all inverse tangent calculations, shows step-by-step solutions, and recognizes special values like tan⁻¹(1) = 45° and tan⁻¹(√3) = 60°.

Question 13

How do you calculate arctan 0.01 in degrees?

Accepted Answer

To calculate arctan 0.01 in degrees: 1) Use arctan(0.01) ≈ 0.009999 radians, 2) Convert to degrees: 0.009999 × (180/π) ≈ 0.573°. Our calculator handles small values like arctan 0.01 with high precision and shows the conversion process step-by-step, making it easy to understand how small angles are calculated.

Query	Exact / Expression	Radians (≈)	Degrees (≈)
tan inverse 0	arctan(0)	0	0°
tan inverse 0.01 in degrees / arctan 0.01	arctan(0.01)	≈ 0.0100 rad	≈ 0.5729°
tan inverse 0.18 in degrees	arctan(0.18)	≈ 0.1781 rad	≈ 10.2041°
tan inverse 0.35 in degrees	arctan(0.35)	≈ 0.3367 rad	≈ 19.2919°
tan inverse 0.625 in degrees	arctan(0.625)	≈ 0.5586 rad	≈ 32.0073°
tan inverse 0.66 in degrees	arctan(0.66)	≈ 0.5834 rad	≈ 33.4175°
inverse tan 2 in degrees	arctan(2)	≈ 1.1071 rad	≈ 63.4349°
tan inverse 6 in degrees	arctan(6)	≈ 1.4056 rad	≈ 80.5377°
arctan(1/6) in degrees	arctan(1/6)	≈ 0.1651 rad	≈ 9.4623°
arctan(1/7) in degrees	arctan(1/7)	≈ 0.1419 rad	≈ 8.1301°

Inverse Tan Calculator (tan⁻¹, arctan)

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