Tan Inverse Calculator

This calculator will help you to calculate the tan inverse of given values in radians or degrees with the steps shown.
Related Calculators:Tan Value Calculator Cot Inverse Calculator

Your Input :-

Your input can be in form of any real number

Formatted User Input Display

\sf{θ:\space \bigg<{-2}\bigg>}

Question

\sf{Calculate \space the \space value \space of \space tan^{-1} \space {-2}}

Step By Step Solution :-

\sf{The \space inverse \space of \space the \space tan \space of \space the \space given \space value \space is \space represented \space as \space \space \space \space \space \space \space \space \space }

\sf{y \space = \space tan^{-1}(x) \space or \space y \space = \space arctan(x) \space or \space y \space = \space atan(x) \space \& \space defined \space by \space a \space function \space such \space that \space x \space = \space tan(y)}

The domain of the tan inverse x is [-1, 1].

\sf{The \space range \space of \space the \space function \space is \space [-{\pi \space \above{1pt}2}, \space {\pi \space \above{1pt}2}].}

Here we will get two types of solutions for this function

\sf{Principal \space Solution:- \space Which \space will \space lie \space under \space the \space range \space of \space the \space function \space i.e. \space [-{\pi \space \above{1pt}2}, \space {\pi \space \above{1pt}2}]. \space }

\sf{General \space Solution: \space - \space it \space will \space have \space values \space from \space – \space ∞ \space to \space + \space ∞ \space so \space the \space general \space solution \space of}

\sf{this \space function \space will \space be \space as \space below.}

\sf{\bold{y = (n\pi + tan^{-1}(x)) }}

where n is an integer & tan^-1(x) represents the principal values of the function only.Step-1

\sf{Given \space value \space x \space = \space {-2} \space }

\sf{Using \space the \space following \space property: \space tan^{-1}(-x) \space = \space -tan^{-1}(x)}

then after putting the value of x

\sf{ tan^{-1}(-2) = -tan^{-1}({2}) = -({7\pi\above{1pt}20}) \space radian \space or \space -63 \space degree}

Final Answer
From the table of the tan values, we can determine the angle such that

\sf{Principal \space Solution \space is \space tan^{-1}({-2}) \space = \space -({7\pi\above{1pt}20}) \space radian \space or \space -63 \space degrees}

\sf{General \space Solution \space is \space tan^{-1}({-2}) \space = \space n\pi \space + \space (-{7\pi\above{1pt}20})}

Where n = 0, ±1, ±2, ±3, …… ∞
Putting n= -2 we get

\sf{Angle \space in \space Radian \space ={{-{47\pi\above{1pt}20}}} \space \& \space Angle \space in \space Degrees \space = \space -423}

Putting n= -1 we get

\sf{Angle \space in \space Radian \space ={{-{27\pi\above{1pt}20}}} \space \& \space Angle \space in \space Degrees \space = \space -243}

Putting n= 0 we get

\sf{Angle \space in \space Radian \space ={{-{7\pi\above{1pt}20}}} \space \& \space Angle \space in \space Degrees \space = \space -63}

Putting n= 1 we get

\sf{Angle \space in \space Radian \space ={{{13\pi\above{1pt}20}}} \space \& \space Angle \space in \space Degrees \space = \space 117}

Putting n= 2 we get

\sf{Angle \space in \space Radian \space ={{{33\pi\above{1pt}20}}} \space \& \space Angle \space in \space Degrees \space = \space 297}

\sf{We \space can \space take \space other \space integral \space values \space of \space n \space to \space obtain \space other \space values}

\sf{of \space the \space angle \space as \space per \space our \space requirement.}

Final Answer

\sf{The \space principal \space value \space of \space tan^{-1}({-2}) \space is \space \bold{-63^{o}} \space or \space \bold{-}\bold{7\pi\above{1pt}20} \space or \space \bold{-1.107radian}.}

\sf{\& \space General \space Solution \space is \space tan^{-1}({-2}) \space = \space \bold{n\pi \space + \space (-{7\pi\above{1pt}20})}}

Note :- If you find any computational or Logical error in this calculator, then you can write your suggestion by clicking the below button or in the comment box.

Get Homework Help

Neetesh Kumar | September 09, 2024 $\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space$ Share this Page on:

1. Introduction to the Tan inverse calculator
2. What is the Formulae used & conditions required ?
3. How do I find the Tan inverse for a given value ?
4. Why choose our Tan inverse Calculator?
5. A Video for explaining this concept
6. How to use this calculator ?
7. Solved Examples
8. Frequently Asked Questions (FAQs)
9. What are the real-life applications?
10. Conclusion

1. Introduction to Tan inverse calculator

Embark on a journey into trigonometry as we explore the tan inverse calculator, often denoted as tan⁻¹ or arctan. This guide aims to unravel the mysteries behind finding the tan inverse value for a given number, providing insights into its application and relevance.
$\bold{Definition}$
Tan inverse is the inverse function of the tangent trigonometric function. It helps us find the angle whose tangent is a given value. With the help of a calculator and inverse, the process becomes quick and efficient.

2. What is the Formulae used & conditions required?

$\bold{Formula \space Used}$
For an angle θ in degrees or radians: Tan⁻¹(θ) = Angle whose tangent is θ. This formula can be easily applied using a tan inverse formula calculator or even manually by understanding the concept.
$\bold{Domain \space and \space Range}$
The domain of the tan inverse is all real numbers, R. The range of tan inverse is from $(-\frac{\pi}{2}, \frac{\pi}{2})$ in radians or (-90°, 90°) in degrees. If you need assistance with these conversions, an inverse tan calculator can help.

$\bold{Table \space of \space Values}$
Here's a quick reference for common tangent values:

Tan Value	Tan $^{-1}(\theta$ )
0	$0^o$
1	$\frac{\pi}{4}$ or $45^o$
$\sqrt{3}$	$\frac{\pi}{3}$ or $60^o$

3. How do I calculate the tan inverse for a given value?

To calculate the tan inverse of a value:

Determine the tangent value for which you want to find the angle.
Use the formula tan⁻¹(θ) = Angle whose tangent is θ. You can either calculate manually or use a tan inverse x calculator for accuracy.
Ensure you use the correct unit—degrees or radians—for the result. If you’re using a calculator, tools like the tan inverse value calculator or the calculator tan⁻¹ can easily guide you through the process.

4. Why choose our tan inverse for a given value calculator?

$\bold{Easy \space \space to \space Use}$
Our tan inverse calculator provides a user-friendly interface that makes it accessible to students and professionals. The process is seamless, whether you're calculating tan inverse 1 value or exploring more complex angles like tan inverse 5.

$\bold{Time \space Saving \space By \space automation}$
Our calculator saves you valuable time and effort. No more manual calculations—enter your value and get the tan inverse calculation within seconds.

$\bold{Accuracy \space and \space Precision}$
Using mathematical formulas, our calculator with tan inverse ensures 100% accuracy, eliminating any errors that might occur with manual calculations.

$\bold{Versatility}$
Our calculator can handle all input values, whether integers, fractions, or real numbers. For instance, if you're calculating tan inverse 5 in degrees, the result is swift and precise.

$\bold{Complementary \space Resources}$
Along with this tool, we offer other resources, including a tan value calculator, an inverse tan calculator in degrees, and other trigonometric tools to enhance your understanding.

5. A video based on how to find the tan inverse for a given value.

6. How to use this calculator

Our tan inverse calculator helps you find the tan inverse of any value. Just input your value, click "Calculate," and a step-by-step solution will be displayed on the screen. You can share, download, or print your results as needed.

7. Solved Example

$\bold{Question:1}$
Find the value of tan $^{-1}(\frac{1}{\sqrt{3}})$ ?
$\bold{Solution}$
tan $^{-1}(\frac{1}{\sqrt{3}})$ = $\frac{\pi}{6}$ or $30^o$

$\bold{Question:2}$
Find the value of tan $^{-1}(\frac{-1}{\sqrt{3}})$ ?
$\bold{Solution}$
tan $^{-1}(\frac{-1}{\sqrt{3}})$ = -tan $^{-1}(\frac{1}{\sqrt{3}})$ = $\frac{-\pi}{6}$ or $-30^o$

8. Frequently Asked Questions (FAQs)

Can tan inverse produce negative values?

Tan inverse can produce positive and negative values based on the input.

Is tan inverse the same as arctan?

Yes, tan inverse is often denoted as tan⁻¹ or arctan.

What is the tan inverse of 0?

The tan inverse of 0 is 0.

Does tan inverse have a periodic nature?

Yes, the tan inverse is periodic with a period of π.

In what real-life scenarios is tan inverse used?

Tan inverse finds applications in physics, engineering, and computer science, particularly in calculating angles and rotations.

9. What are the real-life applications?

In robotics, the tan inverse function is crucial for calculating the angles of joints in robotic arms, ensuring precise movements. Whether it's the tan inverse of 3 or calculating angles for a complex machine, this function simplifies it.

10. Conclusion

Exploring the tan inverse function opens doors to understanding angles in new ways. Tools like the tan inverse calculator make finding values like tan inverse 1 or tan inverse of 0 effortless. Whether you're solving complex trigonometric problems or working on engineering projects, the tan inverse function is an indispensable tool. Mastering its use will empower you to solve real-world challenges with confidence.

If you have any suggestions regarding the improvement of the content of this page, please write to me at My Official Email Address: doubt@doubtlet.com

$\fcolorbox{black}{lightpink}{\color{blue}{Click here to Ask any Doubt}}$
Are you Stuck on homework, assignments, projects, quizzes, labs, midterms, or exams?
To get connected to our tutors in real-time. Sign up and get registered with us.

$\color{red} \bold{Related \space Calculators}$

Sin inverse
Cos inverse
Cot inverse
Sec inverse
Cosec inverse
Calculate Tan value
Hyperbolic Tan value
Inverse Hyperbolic Tan value