# Cosine, sine and tangent in R

R introduction Mathematical functions

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().