arcSin and arcCos without using library functions

Posted on 2009-05-03
Medium Priority
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
  • 2
LVL 85

Accepted Solution

ozo earned 1000 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 1000 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 http://mathworld.wolfram.com/InverseSine.html.

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.

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