# Exercise 4: R trigonometric functions

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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.

##
**Answer 1: click to reveal**

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()

##
**Answer 2: click to reveal**

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()

To

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