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Built-in Trigonometric functions in R

Trigonometric functions are the part of built-in mathematical functions. All these functions are vectorised. In this tutorial you will learn some built-in trigonometric functions in R and how to use these trigonometric functions in R.

Built-in Trigonometric functions

Commonly used trigonometric functions in R are listed below:

Function Operation Performed
sin(x) sine value of x
cos(x) cosine value of x
tan(x) tangent value of x
asin(x) arc-sine value of x
acos(x) arc-cosine value of x
atan(x) arc-tangent value of x
sinh(x) hyperbolic sine of x
cosh(x) hyperbolic cosine of x
tanh(x) hyperbolic tangent of x
asinh(x) hyperbolic arc-sine of x
acosh(x) hyperbolic arc-cosine of x
atanh(x) hyperbolic arc-tangent of x

Examples of Trigonometric functions

R uses the argument to the trigonometric functions sin(), cos() and tan() in radians.

sin() function in R

To compute the $\sin(30^o)$ in R, we need to convert degree to radian as $30^o = \frac{30*\pi}{180}$ radian.

# compute sine of 30 degree angle
sin(30*pi/180)
[1] 0.5

Note that pi is Special constant in R.

cos() function in R

To compute the $\cos(45^o)$ in R, we need to convert degree to radian as $45^o = \frac{45*\pi}{180}$ radian.

# compute cos of 45 degree angle
cos(45*pi/180)
[1] 0.7071068

tan() function in R

To compute the $\tan(60^o)$ in R, we need to convert degree to radian as $60^o = \frac{60*\pi}{180}$ radian.

# Compute tan of 60 degree angle
tan(60*pi/180)
[1] 1.732051

R always works with angles in radian and not degrees. So remember to convert the angle from degree to radian while calculating trigonometric functions.

Examples of Inverse Trigonometric functions

The inverse function returns the angle in radian. To convert it into degree, multiply the answer by $180/\pi$.

asin() function in R

# Compute sin inverse of 0.5.
asin(0.5)*180/pi
[1] 30

acos() function in R

# Compute cos inverse of 0.7071068.
acos(0.7071068)*180/pi
[1] 45
# Compute tan inverse of 60 degree
atan(1.732051)*180/pi
[1] 60

The result of the inverse trigonometric function is in radians. To get it the result in degrees multiply the result by $180/\pi$.

Examples of Hyperbolic Trigonometric functions

sinh() function in R

The hyperbolic sine of $x$ is given by

 $$\sinh (x)=\frac{e^x- e^{-x}}{2}$$

sinh(30*pi/180)
[1] 0.5478535

cosh() function in R

The hyperbolic cosine of $x$ is given by

 $$\cosh (x)=\frac{e^x+ e^{-x}}{2}$$

cosh(45*pi/180)
[1] 1.324609

tanh() function in R

The hyperbolic tangent of $x$ is given by

 $$\tanh (x)=\frac{e^x- e^{-x}}{e^x+ e^{-x}}$$

tanh(60*pi/180)
[1] 0.7807144

Examples of Inverse Hyperbolic Trigonometric functions

asinh() function in R

The inverse hyperbolic sine of $x$ is given by

 $$\text{asinh} (x) =\ln (x+\sqrt{x^2+1})$$

To compute the inverse of sine hyperbolic of 0.5478535, use the following function. Multiplying the result by $180/\pi$ gives you angle in degree.

asinh(0.5478535)*180/pi
[1] 30

acosh() function in R

The inverse hyperbolic cosine of $x$ is given by

 $$\text{acosh} (x)=\ln (x+\sqrt{x^2-1}), x\geq 1$$

To compute the inverse of cosine hyperbolic of 1.324609, use the following function. Multiplying the result by $180/\pi$ gives you angle in degree.

acosh(1.324609)*180/pi
[1] 44.99999

atanh() function in R

The inverse hyperbolic tangent of $x$ is given by

 $$\text{atanh} (x)=\frac{1}{2}\ln \bigg(\frac{1+x}{1-x}\bigg), |x| < 1$$
To compute the inverse of cosine hyperbolic of 2.509178, use the following function. Multiplying the result by $180/\pi$ gives you angle in degree.

atanh(0.7807144)*180/pi
[1] 59.99999

Endnote

In this tutorial you learned about trigonometric functions in R and how to use these functions in R.