Exercise 4: R trigonometric functions

Find a function FUN that leads to the following output:

curve(FUN, from = -10, to = 10, col = "red", ylim = c(-2, 2))
curve(sin, add = TRUE)
grid()

Hint: aim to keep the answer simple. The main logic of the function can often be summarized in a single line of R code.

We can write the function as follows:

  FUN <- function(x) {
    return(sin(x + pi / 2))
  }

We then get:

  curve(FUN, from = -10, to = 10, col = "red", ylim = c(-2, 2))
  curve(sin, add = TRUE)
  grid()

We can use various trigonometric identities to derive more solutions to this puzzle. For example:

sin(x + pi/2) = cos(x)

FUN can then be defined as:

  FUN <- function(x) {
    return(cos(x))
  }

We can confirm that this function solves the puzzle:

  curve(FUN, from = -10, to = 10, col = "red", ylim = c(-2, 2))
  curve(sin, add = TRUE)
  grid()