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

Examples:

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 π/2

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

The PI() function returns the value of pi, and dividing it by 2 gives you the value of π/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

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 -π to π 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

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

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

Examples: