Calculate Sine and Cosine in Excel. Formulas and Examples

In this article we will tell you how to calculate sine and cosine in excelIt's important to note that Excel uses radians for all of its trigonometric functions. If you're working with angles in degrees, you'll need to convert them to radians before entering those values ​​into one of these functions. Read on to learn what formulas are used to build the tables.

Sine and cosine functions in Excel

Below we mention the purpose of some of the most important trigonometric functions in Excel:

• The SIN function in Excel is used to calculate the sine of a given angle in radians and returns the corresponding value.
• The SINH function in Excel returns the hyperbolic sine value of a given real number.
• The COS function in Excel calculates the cosine of an angle specified in radians and returns the corresponding value.
• The COSH function returns the hyperbolic cosine value of the given real number.

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Examples of using the sin, sinh, cos and cosh functions in Excel

Below you will see some examples where sine and cosine calculations are performed in Excel:

Example 1

A traveler climbs a mountain with a slope of 17°. The speed is constant and is 4 km/h. Determine at what height relative to the initial reference point he will be after 3 hours. Data table:

To solve use the formula:

=B2*B3*SIN(RADIANS(B1))

Plot Description:

• B2 * B3 – product of speed and There of a trip, the result of which is the distance traveled (hypotenuse of a right triangle).
• SIN(Radians(B1)) is the sine of the gradient expressed in radians using the RADIANS function.

As a result of the calculations, we obtained the value of the small leg of a right triangle, which characterizes the height of the traveler.

Table of sines and cosines in excel

In the past, reference books for trigonometric functions were widely used in educational institutions. How can I create my own simple reference book using Excel for cosines of angles from 0 to 90? Fill the columns with angles in degrees:

To complete, use the function COS as an array formula. An example to fill the first column:

=COS(RADIANS(A2))

Calculate the values ​​for all angles. The result:

Nota: is known cos(90°) = 0, but the function RADIANS (90) determines the value of the angle radians with some error, therefore, a non-zero value was obtained for the angle of 90°. Similarly, create a sine table in Excel:

Plotting sinh and cosh functions in excel

Construct graphs of the functions sinh (x) and cosh (x) for the same values ​​of the independent variable and compare them. Initial data:

The formula for finding hyperbolic sines:

= SINH (A2)

The formula for finding hyperbolic cosines is:

=COSH(A2)

Table of values ​​obtained:

We build the graph of both functions based on the available data. Select the range of cells A1: C12 and then select the tool «INSERT»-«Charts» -«Insert a scatter chart (X,Y) or bubbles»-«Scatter with soft lines and markers":

As you can see, the graphs coincide in the interval (0;+∞), and in the area of ​​negative X values, parts of the graphs are mirror images of each other.

Features of using trigonometric functions sine and cosine in Excel

Below we describe each of the functions:

SIN function syntax:

= SIN (number)

SINH Function Syntax:

= SINH (number)

COS Function Syntax:

= COS (number)

COSH Function Syntax:

= COSH (number)

Each of the above functions takes a single number argument that characterizes the angle specified in radians (for Sine and Cosine in Excel) or any value in the range of real numbers for which you want to determine the hyperbolic sine or cosine (for SINH and COSH, respectively).

Notes 1:

If as an argument to any of the functions in question Text data was passed that cannot be converted to a numeric value, the result of the functions will be the error code #WORTHFor example, the function =SIN("1") will return the result 0.8415, because Excel performs data conversion whenever possible.

Logical values ​​can be passed as arguments to the functions in question. true and false, which will be interpreted as numeric values ​​1 and 0, respectively. All the functions considered can be used as array formulas.

Notes 2:

1. The hyperbolic sine is calculated by the formula: sinh(x)=0,5*(ex-ex).
2. The formula to calculate the hyperbolic cosine is: cosh(x)=0,5*(ex+ex).
3. When calculating the sines and cosines of angles using the SIN and COS formulas, It is necessary to use angle measurements in radians. If the angle is specified in degrees, the following formula can be used:

Take a look at: Ways to calculate distances between coordinates in Excel

Final thoughts

Done, we now know how to calculate sine and cosine in Excel. In trigonometry there are also inverse functions, which are normally indicated with a superscript -1 in math (i.e. ASIN is Excel's function for sin-1). These will return an angle given a sine (or cosine, tangent, etc.) value. We hope you enjoyed our article; you can let us know via the comments section.