# What is Arctangent: Definition and 17 Discussions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

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1. ### I Finding the inverse tangent of a complex number

Let z=x+iy, and w=u+iv. I am looking for a formula to find the arctangent of z, or w=arctan(z). I want the results of u and v to be in terms of trigonometric and hyperbolic functions (and their inverses) and not in terms of logarithms. The values u and v should be functions of x and y.
2. ### Studying the convergence of a series with an arctangent of a partial sum

Greeting I'm trying to study the convergence of this serie I started studying the absolute convergence because an≈n^(2/3) we know that Sn will be divergente S=∝ so arcatn (Sn)≤π/2 and the denominator would be a positive number less than π/2, and because an≈n^(2/3) and we know 1/n^(2/3) >...
3. ### I Phase angle of a damped driven harmonic oscillation

Hello, in every book and on every website (e.g. here http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) i found for driven harmonic osciallation the same solution for phase angle:θ=atan(ωb/(k−mω^2)) where ω is driven freq., m is mass, k is spring constant. I agree with it =it follows...
4. ### Computing arctan (inverse tan) function

Homework Statement Hello! Surprisingly I get different results when I try to compute the inverse tangent function. My goal is to compute it both manually and using calculator in radiant mode. Homework Equations My goal is to compute arctan(½) both manually and using calculator in radiant...
5. ### I Is there an equivalent form for arctan?

Hi, I was just looking at an example for a certain problem and noticed that in the second step they went to arctan(epsilon). I know there's a form that is equal to arctan but am a little unsure. I've come across formulas on the web such as arctan(x) = ∫(dt)/(a2+t2) but nothing else that would...
6. ### How do I calculate inverse trig functions?

On the paper I'm reading the arctan of 35 over 65 is approx. 28.30degrees. When I use the Google calculator "arctan(35/65)" gives me 0.493941369 rad. What am I doing wrong?
7. ### Conundrum of Solving True Anomaly in Binary Orbits: A Scientist's Dilemma

I have a real doosy that has got me stumped. I need to solve the following equation for v: tan(v + ω) = tan(θ + Ω)sec(i) The symbols stand for the following values in an elliptical orbit of one point source around another (on the celestial sphere): where v = true anomaly; ω = argument of...
8. ### What went wrong in evaluating this integral?

What did I do wrong evaluating this integral: ∫ [4 / (4x^2 + 4x + 65) dx ? Here were my steps: 1) = 4 ∫ [1 / (4x^2 + 4x + 65)] dx 2) = 4 ∫ [1 / (4x^2 + 4x + 1 + 64)] dx 3) = 4 ∫ [1 / ((2x+1)^2 + 64)] dx ; Then I applied the formula: ∫ [1 / √(a^2 + u^2)] dx = (1/a)arctan(u/a) + C; 4) =...
9. ### Approximating Arctangent and Natural Log

I have posted this on other forums, and I have discussed this with my professors, but I thought I would share it here for those interested. Essentially, I have a function that efficiently approximates arctangent on [-1,1] and ln(1+x) on [0,1]. For some background about me, I am a Z80...
10. ### MHB A generalized Arctangent integral/function

This is NOT a tutorial, so by all means, if you've a mind to, the please DO very much feel free to contribute...Preamble:As a consequence of various families of definite integrals I've been studying recently, I've been led to consider what I've come to call the q-shifted Inverse Tangent Integral...
11. ### Manually calculate Arccosine and Arctangent

How do you calculate Arccosine and Arctangent if you do not have a scientific calculator. \theta = atan(\frac{y}{x}) \theta2 = acos(\frac{z}{\sqrt{x^2+y^2+z^2}})
12. ### MHB Limit of Arctan (x^2-4)/(3x^2-6x) as x Approaches 2

Here is the question: Here is a link to the question: What is the limit of arctan( (x^2-4) / (3x^2-6x) ) as x approaches 2? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
13. ### How to prove the definition of arctangent function using integral?

Homework Statement This is a problem from Introduction to Analysis by Arthur P. Mattuck,chapter 20,problem 20-1. <a href="http://www.flickr.com/photos/86024731@N04/8090259684/" title="arctangent by gnu is not unix, on Flickr"><img...
14. ### Convergence of the Arctangent Integral

Homework Statement Is $\intop_{-\infty}^{\infty}\arctan(x)\, dx$ convergent? What about $\lim_{t\rightarrow\infty}\intop_{-t}^{t}\arctan(x)\, dx$?Homework Equations The Attempt at a Solution I think the first integral may actually be divergent the way its written and the second one...
15. ### Help Calculating Pi using Arctangent formula

Homework Statement Using the Arctangent formula pi = 16 * arctan (1 / 5) - 4*arctan(1 / 239) to calculate the value of pi to 53 significant digits.Homework Equations The power series of arctangent(x) is = x − x^3/3 + x^5/5 − x^7/7 + x^9/9... The Attempt at a Solution...
16. ### Finding the Arctangent of an Unknown Number

How do you go about finding the arctangent of an unfamiliar number. Example, arctan (-2)? I think it's in the direction of half-angles and double angels, but how do I get the angle to start with the formulas in the first place? Thanks in advance!
17. ### Compute Arctangent Series: Sum from 0 to n

I am trying to compute: \sum_{k=0}^{n}\arctan{\left(\frac{1}{k^{2}+k+1}\right)}. I have used some trig identities and reduced it, but before I can do anything more I am stuck on: \sum_{k=0}^{n}\arctan{\left(k\right)}. Is there a formula for this sum? Thanks for the help.