# Excel Trigonometric Functions with Examples

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles. In this article, we will explore the different Excel trigonometric functions with examples and how they can be used to perform calculations involving angles and triangles.

## Theories you Should know about Trigonometry

## Basic Trigonometric Functions in Excel

Syntax | =SIN( N) | =COS( N) | =TAN( N) |

Argument | N is an angle in radians | ||

Return | Calculated sine of the given angle | Calculated cosine of the given angle | Calculated tangent of the given angle |

Examples:

Syntax | =SEC( N) | =CSC( N) | =COT( N) |

Argument | N is an angle in radians | ||

Return | Calculated secant of the given angle | Calculated cosecant of the given angle | Calculated cotangent of the given angle |

## Does Excel do Trigonometric Functions in Radians or Degrees?

The trigonometric functions in Excel, such as** SIN**, **COS**, and **TAN**, by default measure angles in radians rather than degrees. Hence, before applying degrees to SIN, COS, TAN, etc., you must convert them into radians if you wish to operate with degrees.

## Converting Degrees to Radians and Vice Versa in Excel

For converting between radians and degrees, Excel has functions. For instance, you can convert an angle from degrees to radians using the RADIANS function, and vice versa using the DEGREES function.

- The Degree to Radians:

`=RADIANS(N) `

where N is the value of the angle in degrees.

- The Radians to Degree:

`=DEGREES(N) `

where N is the value of the angle in radians.

Please, See the example below,

### How do you write sin 90 in Excel?

To calculate the sine of 90 degrees in Excel, you can use the** SIN** function with the argument of** Ï€/2**

`=SIN(PI()/2) //returns 1`

The** PI() **function returns the value of pi, and dividing it by 2 gives you the value of **Ï€/2**. This will return the value of 1, which is the sine of 90 degrees

Or you can convert 90 degrees to radians using the formula below,

`=SIN(RADIANS(90)) //returns 1`

**Inverse** Trigonometric Functions **in** Excel

Syntax | =ASIN( N) | =ACOS( N) | =ATAN( N) |

Argument | N is a number in the range -1 to 1 | ||

Return | Calculated inverse sine or ArcSine in radians of the given number | Calculated inverse cosine or ArcCoine in radians of the given number | Calculated inverse tangent or ArcTangent in radians of the given number |

Similarly, you can find the inverse of **COT** by applying the **ACOT(N)** functions.

Examples:

## Practical Example: Excel Calculate Angle of Triangle

Suppose you have to find all angles in the image given below.

Here, Base and Height are 3M and 5M respectively

According to Pythagoras’ theorem,

Where,

c= Hypotenuse

a = Base

b= Height

You can calculate the value of Hypotenuse using the following formula

`=SQRT(5^2+3^2) //returns 5.830952`

Calculate angle in degrees using the following formula

`=DEGREES(ATAN(5/3)) //returns`

## Difference Between ATAN and ATAN2 Functions in Excel:

The ATAN function can be used to determine the arctangent of a single integer. However, the ATAN2 function should be used if you need to calculate angles depending on an object’s position in a cartesian plane.

### Syntax of ATAN2 Function

` =ATAN2(y, x)`

Where, the y-coordinate and x-coordinate of the point for which you want to calculate the arctangent

### Return of ATAN2 Function

The **ATAN2** function returns the arctangent of **y/x** in radians, with a range of -Ï€ to Ï€ radians (-180 to 180 degrees). The result is expressed as a positive or negative angle, depending on the signs of x and y.

Examples:

`=ATAN2(4, 3) //returns 0.643501109`

## Hyperbolic Trigonometric Functions in Excel

Syntax | =SINH( N) | =COSH( N) | =TANH( N) |

Argument | N is a real number | ||

Return | Calculated hyperbolic sine of the given number | Calculated hyperbolic cosine of the given number | Calculated hyperbolic tangent of the given number |

Similarly, you can calculate hyperbolic secant, cosecant, cotangent of the given number using **SECH( N), CSCH( N)**, and **COTH( N)** functions respectively

Examples:

## Inverse Hyperbolic Trigonometric Functions in Excel

Syntax | =ASINH( N) | =ACOSH( N) | =ATANH( N) |

Argument | N is a real number | ||

Return | Calculated inverse hyperbolic sine of the given number | Calculated inverse hyperbolic cosine of the given number | Calculated inverse hyperbolic tangent of the given number |

Similarly, you can calculate inverse hyperbolic cotangent of the given number using and **ACOTH( N) **functions respectively

Examples: