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4.8.2 Trigonometric functions
cl_R sin (const cl_R& x)

Returns
sin(x)
. The range of the result is the interval1 <= sin(x) <= 1
. cl_N sin (const cl_N& z)
Returns
sin(z)
. The range of the result is the entire complex plane.cl_R cos (const cl_R& x)

Returns
cos(x)
. The range of the result is the interval1 <= cos(x) <= 1
. cl_N cos (const cl_N& x)
Returns
cos(z)
. The range of the result is the entire complex plane.struct cos_sin_t { cl_R cos; cl_R sin; };
cos_sin_t cos_sin (const cl_R& x)
Returns both
sin(x)
andcos(x)
. This is more efficient than computing them separately. The relationcos^2 + sin^2 = 1
will hold only approximately.cl_R tan (const cl_R& x)
cl_N tan (const cl_N& x)
Returns
tan(x) = sin(x)/cos(x)
.cl_N cis (const cl_R& x)
cl_N cis (const cl_N& x)
Returns
exp(i*x)
. The name ‘cis’ means “cos + i sin”, becausee^(i*x) = cos(x) + i*sin(x)
.cl_N asin (const cl_N& z)
Returns
arcsin(z)
. This is defined asarcsin(z) = log(iz+sqrt(1z^2))/i
and satisfiesarcsin(z) = arcsin(z)
. The range of the result is the strip in the complex domainpi/2 <= realpart(arcsin(z)) <= pi/2
, excluding the numbers withrealpart = pi/2
andimagpart < 0
and the numbers withrealpart = pi/2
andimagpart > 0
.cl_N acos (const cl_N& z)

Returns
arccos(z)
. This is defined asarccos(z) = pi/2  arcsin(z) = log(z+i*sqrt(1z^2))/i
and satisfiesarccos(z) = pi  arccos(z)
. The range of the result is the strip in the complex domain0 <= realpart(arcsin(z)) <= pi
, excluding the numbers withrealpart = 0
andimagpart < 0
and the numbers withrealpart = pi
andimagpart > 0
. cl_R atan (const cl_R& x, const cl_R& y)
Returns the angle of the polar representation of the complex number
x+iy
. This isatan(y/x)
ifx>0
. The range of the result is the intervalpi < atan(x,y) <= pi
. The result will be an exact number only ifx > 0
andy
is the exact0
. WARNING: In Common Lisp, this function is called as(atan y x)
, with reversed order of arguments.cl_R atan (const cl_R& x)
Returns
arctan(x)
. This is the same asatan(1,x)
. The range of the result is the intervalpi/2 < atan(x) < pi/2
. The result will be an exact number only ifx
is the exact0
.cl_N atan (const cl_N& z)
Returns
arctan(z)
. This is defined asarctan(z) = (log(1+iz)log(1iz)) / 2i
and satisfiesarctan(z) = arctan(z)
. The range of the result is the strip in the complex domainpi/2 <= realpart(arctan(z)) <= pi/2
, excluding the numbers withrealpart = pi/2
andimagpart >= 0
and the numbers withrealpart = pi/2
andimagpart <= 0
.
Archimedes’ constant pi = 3.14… is returned by the following functions:
cl_F pi (float_format_t f)

Returns pi as a float of format
f
. cl_F pi (const cl_F& y)
Returns pi in the float format of
y
.cl_F pi (void)
Returns pi as a float of format
default_float_format
.
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