OpenEuphoria

trig_range

include arcsin.e 
public type trig_range(object x) 

values passed to arccos and arcsin must be in the inclusive range [-1,+1]

arcsin

include arcsin.e 
public function arcsin(trig_range x) 

returns an angle in a right triangle given its sine.

Arguments:

1. trig_range : an atom or a sequence of atomic items; each value is a trig_range ratio.

Returns:

An object, the same shape as trig_range, each atom is an angle measured in radians.

Errors:

The arcsin function requires arguments in the inclusive [ -1..1 ] range; a typecheck error occurs otherwise.

Comments:

 
             /|   
hypotenuse c/ | a opposite  
           /__| 
          A  b adjacent 
      angle 
 
 The right triangle abc 

The arcsin (angle in radians) is the inverse function of the sin (ratio of a/c ) function .

The argument to the arcsin function must be in the inclusive range of -1 to +1 .

The return value is an angle, measured in radians, in the inclussive range of -PI/2 to +PI/2 .

The arcsin may be applied to an atom or to all atomic items in a sequence.

Note:

The arcsin function is not as fast as the arctan function.

Example 1:

s = arcsin({-1,0,1}) 
? s 
--> {-1.570796327, 0, 1.570796327} 
 
include std/mathcon.e 
? PI/2 
--> 1.570796327 

Example 2:

In the right triangle

 
             /|   
hypotenuse 5/ | 4 opposite  
           /__| 
          A  3 adjacent 
      angle 
 
 The right triangle abc 

the sine of A is opposite/hypotenuse. Given the ratio 4/5, what is the angle A in radians?

                                                     include std/math.e 
atom r = arcsin( 4/5 ) 
? r 
--> 0.927295218 
r = rad2deg(r) 
? r 
--> 53.13010235 

See Also:

arccos | arctan | sin | PI | rad2deg | deg2rad