Arctangent Definition and 17 Threads

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.

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) >...

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...

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...

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...

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?

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...

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) =...

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...

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...

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}})

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.

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...

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...

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...

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!

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.