# Arctangent

### A Direct Proof of the Integral Formula for Arctangent

A Direct Proof of the Integral Formula for Arctangent Arnold J. Insel, Illinois State University, Normal, IL The College Mathematics Journal, May 1989, Volume 20, Number 3, pages 235-237.

### Efficient Approximations for the Arctangent Function

FOUR QUADRANT APPROXIMATIONS The arctan algorithms presented thus far are applicable for angles in the range of − π/ 4to π/ 4rad. Here we extend the angular range to − π to π radians.

### A Sequence of Polynomials for Approximating Arctangent

NOTES Edited by William Adkins A Sequence of Polynomials for Approximating Arctangent Herbert A. Medina 1. INTRODUCTION. The Taylorseries arctan x = x − x 3 3 + x 5 5 −+···= ∞ * k =0 ( −1 ) k 2 k +1 x 2 k +1 was discovered by the Scotsman James Gregory in 1671[ 1 , chap. 12].

### A Guide to Approximations

Arctangent, arcsine and arccosine The arctangent is the same as the inverse tangent, so arctan(tan(x))=x. It's often denoted as "atan(x)" or "tan-1 (x)".

### The Arctangent Approach of Digital PGC Demodulation for Optic ...

The Arctangent Approach of Digital PGC Demodulation for Optic Interferometric Sensors Liwei Wang*, Min Zhang, Xianhui Mao, Yanbiao Liao Department of Electronic Engineering, Tsinghua University, Beijing, China, 100084 ABSTRACT The development of the optic interferometric sensors is partly ...

### Mathematical Techniques

PART FOUR Formulas FM 5-33 Mathematical Techniques Chapter 10 GEOMETRIC FUNCTIONS The result of any operation performed by terrain analysts will only be as accurate as the measurements used.

### Some properties of the Arctangent Distribution

S tatistica & A pplicazioni Vol. 2, n. 1, 2004 Some properties of the Arctangent Distribution Angiola Pollastri § Franco Tornaghi ‡ Summary: In the present paper some characteristics of the Arctangent Distribution are analysed.

### Economic Valuation Models for Insurers

At two of the nodes, we have shown how the cash flows may be modeled using an arctangent lapse function fitted to lapse data. Depending on where along the arctangent curve the interest rate spreads lie, ...

### MODELING SURRENDER/LAPSE RATES AND VALUING SURRENDER OPTIONS ...

• For Arctangent model, the probability of surrender s q is, s q = a+b Arctangent(m DIFFLAG0 -n) (5) where a,b,m, and n are coefficients to be ...

### Pricing Mortgage-backed Securities and Collateralized ...

In our simulation, we will use a slight variation of the arctangent function. The curve in Figure 1 displays the pure refinancing incentive for our prepayment model.