These functions give the obvious trigonometric functions. They respectively compute the cosine, sine, tangent, arc-cosine, arc-sine, arc-tangent, and the two-argument arc-tangent.
cospi(x), sinpi(x), and tanpi(x), compute
cos(pi*x), sin(pi*x), and tan(pi*x).
Value
tanpi(0.5) is NaN. Similarly for other inputs
with fractional part 0.5.
Details
The arc-tangent of two arguments atan2(y, x) returns the angle
between the x-axis and the vector from the origin to \((x, y)\),
i.e., for positive arguments atan2(y, x) == atan(y/x).
Angles are in radians, not degrees, for the standard versions (i.e., a
right angle is \(\pi/2\)), and in ‘half-rotations’ for
cospi etc.
cospi(x), sinpi(x), and tanpi(x) are accurate
for x values which are multiples of a half.
All except atan2 are internal generic primitive
functions: methods can be defined for them individually or via the
Math group generic.
These are all wrappers to system calls of the same name (with prefix
c for complex arguments) where available. (cospi,
sinpi, and tanpi are part of a C11 extension
and provided by e.g. macOS and Solaris: where not yet
available call to cos etc are used, with special cases
for multiples of a half.)
Examples
x <- seq(-3, 7, by = 1/8)
tx <- cbind(x, cos(pi*x), cospi(x), sin(pi*x), sinpi(x),
tan(pi*x), tanpi(x), deparse.level=2)
#> Warning: NaNs produced
op <- options(digits = 4, width = 90) # for nice formatting
head(tx)
#> x cos(pi * x... cospi(x) sin(pi * x... sinpi(x) tan(pi * x... tanpi(x)
#> [1,] -3.000 -1.000e+00 -1.0000 -3.674e-16 0.0000 3.674e-16 0.0000
#> [2,] -2.875 -9.239e-01 -0.9239 -3.827e-01 -0.3827 4.142e-01 0.4142
#> [3,] -2.750 -7.071e-01 -0.7071 -7.071e-01 -0.7071 1.000e+00 1.0000
#> [4,] -2.625 -3.827e-01 -0.3827 -9.239e-01 -0.9239 2.414e+00 2.4142
#> [5,] -2.500 3.062e-16 0.0000 -1.000e+00 -1.0000 -3.266e+15 NaN
#> [6,] -2.375 3.827e-01 0.3827 -9.239e-01 -0.9239 -2.414e+00 -2.4142
tx[ (x %% 1) %in% c(0, 0.5) ,]
#> x cos(pi * x... cospi(x) sin(pi * x... sinpi(x) tan(pi * x... tanpi(x)
#> [1,] -3.0 -1.000e+00 -1 -3.674e-16 0 3.674e-16 0
#> [2,] -2.5 3.062e-16 0 -1.000e+00 -1 -3.266e+15 NaN
#> [3,] -2.0 1.000e+00 1 2.449e-16 0 2.449e-16 0
#> [4,] -1.5 -1.837e-16 0 1.000e+00 1 -5.444e+15 NaN
#> [5,] -1.0 -1.000e+00 -1 -1.225e-16 0 1.225e-16 0
#> [6,] -0.5 6.123e-17 0 -1.000e+00 -1 -1.633e+16 NaN
#> [7,] 0.0 1.000e+00 1 0.000e+00 0 0.000e+00 0
#> [8,] 0.5 6.123e-17 0 1.000e+00 1 1.633e+16 NaN
#> [9,] 1.0 -1.000e+00 -1 1.225e-16 0 -1.225e-16 0
#> [10,] 1.5 -1.837e-16 0 -1.000e+00 -1 5.444e+15 NaN
#> [11,] 2.0 1.000e+00 1 -2.449e-16 0 -2.449e-16 0
#> [12,] 2.5 3.062e-16 0 1.000e+00 1 3.266e+15 NaN
#> [13,] 3.0 -1.000e+00 -1 3.674e-16 0 -3.674e-16 0
#> [14,] 3.5 -4.286e-16 0 -1.000e+00 -1 2.333e+15 NaN
#> [15,] 4.0 1.000e+00 1 -4.899e-16 0 -4.899e-16 0
#> [16,] 4.5 5.511e-16 0 1.000e+00 1 1.815e+15 NaN
#> [17,] 5.0 -1.000e+00 -1 6.123e-16 0 -6.123e-16 0
#> [18,] 5.5 -2.450e-15 0 -1.000e+00 -1 4.082e+14 NaN
#> [19,] 6.0 1.000e+00 1 -7.348e-16 0 -7.348e-16 0
#> [20,] 6.5 -9.803e-16 0 1.000e+00 1 -1.020e+15 NaN
#> [21,] 7.0 -1.000e+00 -1 8.573e-16 0 -8.573e-16 0
options(op)