# لنفترض أن$\ dot {x} =\arctan (x (t)\cdot t)$،$x (t_0) = x_0$يكون IVP. أثبت أنه إذا كان$x_0 <0$، فإن$x (t) <0$للجميع$\ mathbb {R}$

## Simplify tan(arctan(x))

I have to calculate the value of arctan(x). I have calculated the value of this by evaluating the following series : Arctan (x) = x – x^3/3 + x^5/5 – x^7/7 + x^9/9 - … But the following code can not calculate the actual value. For example, calculate_angle(1) returns 38.34 . Why? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Inverse trigonometric functions In other words, atan2(y, x) is the angle between the positive x-axis of a plane and the point (x, y) on it, with positive sign for counter-clockwise angles (upper half-plane, y > 0), and negative sign for clockwise angles (lower half-plane, y < 0). It was first introduced in many computer programming languages, but it is now also common in ... Calculating the value of arctan(x) in C++ ArcTan—Wolfram Language Documentation Efficient Approximations for the Arctangent Function T ArcTan is the inverse tangent function. For a real number x, ArcTan [x] represents the radian angle measure such that .The two-argument form ArcTan [x, y] represents the arc tangent of y / x, taking into account the quadrant in which the point lies. It therefore gives the angular position (expressed in radians) of the point measured from the positive axis. ... IEEE SIGNAL PROCESSING MAGAZINE [109] MAY 2006 arctan(x) ≈ π 4 x, −1 ≤ x ≤ 1.(2) This linear approximation has been used in [6] for FM demodulation due to its minimal complexity.