Inverse Trigonometric Functions
DESCRIPTION:
Performs inverse trigonometric transformations of real or complex numbers.
USAGE: 
acos(x)
asin(x)
atan(x)
atan(x, y)
REQUIRED ARGUMENTS:
x:
numeric or complex. Missing values (NAs) are allowed.
y:
numeric, same length as x. Missing values (NAs) are allowed.
VALUE:
data transformed (to radians) by the specified inverse trigonometric function, with attributes preserved.
CLASSES:
This function will be used as the default method for classes that do not inherit a specifc method for the function or for the Math group of functions. The result will retain the class and the attributes. If this behavior is not appropriate, the designer of the class should provide a method for the function or for the Math group.
DETAILS:
For atan with two arguments, both arguments should be numeric. When x^2+y^2==1, the return value satisfies cos(atan(x,y))==y and sin(atan(x,y))==x. That is, atan(n,d) (the quadrant correct arctangent) is equal to atan(n/d) when d is positive. Notice that there is a potential confusion in the naming of the arguments in this form of atan, as it usual to think of cos being associated with the x coordinate and sin with the y coordinate. Thus, for example, Arg(1-1i) is the same as atan(-1,1) and not atan(1,-1). To put it another way, Arg(z) is the same as atan(Im(z),Re(z)).

For numeric arguments, the domain of acos and asin is the interval [-1, 1], and the range is 0 <= acos(x) <= pi and -pi/2 <= asin(x) <= pi/2. The domain of atan is unrestricted and the range is -pi/2 < atan(x) < pi/2 or -pi < atan(x,y) <= pi. For values of the arguments outside of the appropriate domains, is returned and a warning is given.

These functions are members of the Math group of generic functions.

For further information on domains and branch cuts in the case of complex arguments, see section 5.1.5 of Becker, Chambers and Wilks.

SEE ALSO:
acosh , cos .
EXAMPLES: 
atan(-1,1) # returns -pi/4
atan(1,-1) # returns 3*pi/4


acos(1/2)  # returns pi/3
disk <-complex(arg = seq(-pi,pi, len = 50))
           #fifty points on a unit circle
asin(disk)