Angle between two vectors

angle calculates the angle between two vectors.

Usage

angle(x, y, degree = TRUE)

Arguments

x

a numeric vector

y

a numeric vector

degree

logical; should the angle be computed in degrees? If FALSE the result is returned in radians

Value

a scalar containing the angle between the vectors

See also

len

Examples

x <- c(2,1)
y <- c(1,1)
angle(x, y) # degrees
#>          [,1]
#> [1,] 18.43495
angle(x, y, degree = FALSE) # radians
#>           [,1]
#> [1,] 0.3217506

# visually
xlim <- c(0,2.5)
ylim <- c(0,2)
# proper geometry requires asp=1
plot( xlim, ylim, type="n", xlab="X", ylab="Y", asp=1,
  main = expression(theta == 18.4))
abline(v=0, h=0, col="gray")
vectors(rbind(x,y), col=c("red", "blue"), cex.lab=c(2, 2)) 
text(.5, .37, expression(theta))



####
x <- c(-2,1)
y <- c(1,1)
angle(x, y) # degrees
#>          [,1]
#> [1,] 108.4349
angle(x, y, degree = FALSE) # radians
#>          [,1]
#> [1,] 1.892547

# visually
xlim <- c(-2,1.5)
ylim <- c(0,2)
# proper geometry requires asp=1
plot( xlim, ylim, type="n", xlab="X", ylab="Y", asp=1,
  main = expression(theta == 108.4))
abline(v=0, h=0, col="gray")
vectors(rbind(x,y), col=c("red", "blue"), cex.lab=c(2, 2)) 
text(0, .4, expression(theta), cex=1.5)