# Cosine, sine and tangent in R

R provides several functions to compute trigonometric functions, such as the sine, cosine, tangent, arc-cosine, arc-sine and arc-tangent with the cos(), sin(), tan(), acos(), asin() and atan() functions. In this tutorial we will review how to compute and plot these functions.

##
Cosine function with `cos`

The cosine for an angle \(x\) is the length of side adjacent to angle \(x\) divided by the length of the hypotenuse. You can use the `cos`

function to compute the cosine function for a single value or a vector of values.

```
cos(1) # 0.5403
cos(0) # 1
cos(pi) # -1
cos(0.5) # 0.8776
cos(-1) # 0.5403
```

The following line of code displays the cosine function from -10 to 10.

`plot(cos, -10, 10, col = 4, main = "cos(x)")`

##
Sine function with `sin`

The sine is the length of the side opposite to angle \(x\) divided by the length of the hypotenuse. The function named `sin`

can be used to compute the sin of an angle, as shown in the examples below.

```
sin(1) # 0.8415
sin(0) # 0
sin(pi/2) # 1
sin(0.5) # 0.4794
sin(-1) # -0.8415
```

Use the following code to visually represent the sine.

`plot(sin, -10, 10, col = 4, main = "sin(x)")`

##
Tangent function with `tan`

The tangent of an angle \(x\) is the length of side opposite angle \(x\) divided by the length of the side adjacent to angle \(x\). In R, you can make use of the `tan`

function to calculate the tangent of an angle.

```
tan(1) # 1.557
tan(0) # 0
tan(pi) # -1.225e-16
tan(0.5) # 0.5463
tan(-1) # -1.557
```

The following line of code can be used to represent the tangent function from \(-2 \pi\) to \(2 \pi\).

`plot(tan, -2 * pi, 2 * pi, col = 4, main = "tan(x)", type = "l")`

##
Arc-cosine function with `acos`

The arccosine is the **inverse function of the cosine** for an angle \(x\). Use the `acos`

function to compute the values as in the examples below.

```
acos(1) # 0
acos(0) # 1.571
acos(pi) # NaN
acos(0.5) # 1.047
acos(-1) # 3.142
```

As the domain of the arccosine ranges from -1 to 1 you can use the following line of code to represent it.

`plot(acos, -1, 1, col = 4, main = "acos(x)")`

##
Arc-sine function with `asin`

The arcsine is the **inverse function of the sine** for an angle \(x\). In R, you can make use of the `asin`

function as in the following block of code.

```
asin(1) # 1.571
asin(0) # 0
asin(pi) # NaN
asin(0.5) # 0.5236
asin(-1) # -1.571
```

The domain of the arcsine also ranges from -1 to 1. Use the following line of code to represent this function.

`plot(asin, -1, 1, col = 4, main = "asin(x)")`

##
Arc-tangent function with `atan`

The arctangent is the inverse of the tangent function for an angle \(x\). Use the `atan`

function in R to compute it.

```
atan(1) # 0.7854
atan(0) # 0
atan(pi) # 1.263
atan(0.5) # 0.4636
atan(-1) # -0.7854
```

Use the following line of code if you want to plot the arctangent function in R:

`plot(atan, -10, 10, col = 4, main = "atan(x)")`

R provides other functions named `cospi()`

, `sinpi()`

and `tanpi()`

that compute `cos(pi*x)`

, `sin(pi*x)`

and `tan(pi*x)`

, respectively.

Angles are in radians for the standard versions, not degrees, and in â€˜half-rotationsâ€™ for `cospi()`

, `sinpi()`

and `tanpi()`

.