arcSin and arcCos without using library functions

Posted on 2009-05-03
Last Modified: 2012-05-06
Hi guys i want to find arcSin and arcCos without using library functions,

Can you please provide me the algorithm or equation which gives accurate reading,

Please help,

its urgent,

Question by:montu_12
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 2
LVL 84

Accepted Solution

ozo earned 250 total points
ID: 24292794
float arctan(float x){
    if( x < 0 ){ return -arctan(-x); }
    if( x > 1 ){ return pi/2 - arctan(1/x); }
    if( x <= 1/8.0 ){ return  0.9974133042 * x; }
    if( x <= 2/8.0 ){ return  0.004072621 + 0.964989344 * x; }
    if( x <= 3/8.0 ){ return .017899968 + 0.910336056 * x; }
    if( x <= 4/8.0 ){ return .044740546 + 0.839015512 * x; }
    if( x <= 5/8.0 ){ return .084473784 + 0.759613648 * x; }
    if( x <= 6/8.0 ){ return .134708924 + 0.679214352 * x; }
    if( x <= 7/8.0 ){ return .192103293 + 0.602631128 * x; }
    if( x <= 8/8.0 ){ return .253371504 + 0.532545304 * x; }

float arcsin(float x){
  return arctan(x/sqrt(1-x*x));
float arccos(float x){
    return pi/2 - arcsin(x);
LVL 27

Expert Comment

ID: 24293128
Arcsin(x) Calculator

Inverse trigonometric functions
You can write a loop to calculate the definite integrals. Divide the area let's say by 1000 and calculate the areas of the smaller 1000s rectangles.

Calculating ArcSin and ArcCos
LVL 27

Expert Comment

ID: 24297091
LVL 22

Assisted Solution

NovaDenizen earned 250 total points
ID: 24306215
I like ozo's code, except for the piecewise linear approximation (all the "if (x <=" lines).  I would instead recommend the Maclaurin series, see (17) at

Alternatively, you will get quicker convergence and better numerical accuracy if you also use the Maclaurin series for arccos(1 - y), for situations when y is close to 1 and convergence will be slow.

Featured Post

Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

726 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question