107 LearnersLast updated on June 28th, 2025
Arctan Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re calculating angles, solving equations, or working on engineering tasks, calculators will make your life easy. In this topic, we are going to talk about arctan calculators.
What is an Arctan Calculator?
An arctan calculator is a tool used to find the angle whose tangent is a given number.
Arctan, short for arc tangent, is the inverse function of the tangent in trigonometry.
This calculator makes it easier and faster to find the angle, saving time and effort in calculations.
How to Use the Arctan Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the tangent value: Input the tangent value into the given field.
Step 2: Click on calculate: Click on the calculate button to find the angle and get the result.
Step 3: View the result: The calculator will display the angle in degrees or radians instantly.
How to Calculate Arctan?
To calculate the arctan of a number, you can use a calculator or specific mathematical tables.
The arctan function is typically denoted as arctan(x) or tan⁻¹(x) and returns the angle whose tangent is x.
The result is usually between -π/2 and π/2 radians or -90° and 90°.
Tips and Tricks for Using the Arctan Calculator
When using an arctan calculator, there are a few tips and tricks to make it easier and avoid mistakes:
Consider the domain of the arctan function, which is all real numbers.
Remember the output range is typically -90° to 90° or -π/2 to π/2.
Use the calculator in both degrees and radians mode, depending on your need.
Common Mistakes and How to Avoid Them When Using the Arctan Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible to make errors when using a calculator.
Mistake 1
Ignoring the Range of Arctan
Ensure that the angle result is within the range of -π/2 to π/2 radians or -90° to 90°.
If the calculator displays a value outside this range, it may be incorrect.
Mistake 2
Confusing Degrees and Radians
Always check whether the calculator is set to degrees or radians.
Using the wrong unit can lead to significant errors in calculations.
Mistake 3
Misinterpreting the Angle
Remember that the arctan function provides angles in the range of -90° to 90°. Misinterpreting this can lead to incorrect assessments in practical applications.
Mistake 4
Over-reliance on the Calculator
While the calculator provides quick results, ensure to understand the concept of arctan and its properties, as the calculator might not provide context-specific insights.
Mistake 5
Assuming Calculator Handles Complex Numbers
Most basic calculators do not handle complex numbers with the arctan function, so ensure to check if your calculator supports complex inputs if needed.
Arctan Calculator Examples
Problem 1
What is the angle whose tangent is 1?
Use the function: Angle = arctan(1) Angle = 45° or π/4 radians The angle whose tangent is 1 is 45° or π/4 radians.
Explanation
The tangent of 45° or π/4 radians is 1, hence arctan(1) equals 45° or π/4 radians.
Problem 2
Find the angle for a tangent value of -√3.
Use the function: Angle = arctan(-√3) Angle = -60° or -π/3 radians The angle corresponding to a tangent value of -√3 is -60° or -π/3 radians.
Explanation
The tangent of -60° or -π/3 radians equals -√3, thus arctan(-√3) provides -60° or -π/3 radians.
Problem 3
Calculate the angle with a tangent value of 0.5.
Use the function: Angle = arctan(0.5) Angle ≈ 26.57° or 0.4636 radians The angle whose tangent is 0.5 is approximately 26.57° or 0.4636 radians.
Explanation
The tangent of approximately 26.57° or 0.4636 radians is 0.5, thus arctan(0.5) gives this angle.
Problem 4
Determine the angle for a tangent value of -1.
Use the function: Angle = arctan(-1) Angle = -45° or -π/4 radians The angle whose tangent is -1 is -45° or -π/4 radians.
Explanation
The tangent of -45° or -π/4 radians is -1, so arctan(-1) results in -45° or -π/4 radians.
Problem 5
What is the angle if the tangent value is √3/3?
Use the function: Angle = arctan(√3/3) Angle = 30° or π/6 radians The angle whose tangent is √3/3 is 30° or π/6 radians.
Explanation
The tangent of 30° or π/6 radians equals √3/3, hence arctan(√3/3) results in 30° or π/6 radians.
FAQs on Using the Arctan Calculator
1.How do you calculate arctan?
2.Is arctan the same as inverse tangent?
3.Why is the arctan range -π/2 to π/2?
4.How do I use an arctan calculator?
5.Is the arctan calculator accurate?
Glossary of Terms for the Arctan Calculator
- Arctan Calculator: A tool used to find the angle whose tangent is a given number.
- Radians: A unit of angle measurement based on the radius of a circle, where 2π radians is a full circle.
- Degrees: A unit of angle measurement where 360 degrees make a full circle.
- Inverse Function: A function that reverses the effect of the original function. In this case, arctan is the inverse of tangent.
- Tangent: A trigonometric function that represents the ratio of the opposite side to the adjacent side in a right triangle.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
