The COS function calculates the cosine of an angle.
1. COS Function Syntax
COS(number)
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2. COS function Arguments
| number |
Required. The radian angle you want to know the cosine of. |
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3. COS function example
Formula in cell C3:
=COS(B3)
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4. How to calculate cosine using degrees
Use the RADIANS function to convert degrees to radians.
Formula in cell C3:
=COS(RADIANS(B3))
Explaining formula
Step 1 - Convert degrees to radians
The RADIANS function converts degrees to radians.
Function syntax: RADIANS(angle)
RADIANS(B3)
becomes
RADIANS(360)
and returns approx. -3.28 or -2*pi.
Step 2 - Calculate the cosine
The COS function calculates the cosine of an angle.
Function syntax: COS(number)
COS(RADIANS(B3))
becomes
COS(-2*pi)
and returns 0 (zero).
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5. How to plot a cosine wave
The image above demonstrates a scatter chart containing a cosine graph. Here is how to create a cosine plot:
The formula in cell C15 creates radians starting from -2*pi and adds (1/4)*pi for each cell below.
Formula in cell C15:
=-2*PI()+(ROW(A1)-1)*PI()/4
Formula in cell D15:
=COS(C15)
5.1 Explaining formula in cell C15
Step 1 - Calculate -2*pi
The PI function returns the number pi, it has no arguments.
-2*PI()
becomes
-2*3.14 (approx.)
and returns approx. -6.28
Step 2 - Subtract with pi/4
The ROW function returns a number representing the row in a cell reference.
ROW(reference)
A1 is a relative cell reference meaning it changes when the cell is copied to cells below, this creates a sequential list of numbers starting from 1 to n.
(ROW(A1)-1)*PI()/4
becomes
(1-1)*PI()/4
becomes
0*PI()/4
and returns 0 (zero).
Step 3 - Calculate radian
-2*PI()+(ROW(A1)-1)*PI()/4
becomes
-6.28 + 0 equals approx. -6.28
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5.2 How to insert a Scatter chart with Smooth Lines and Markers
- Select cell range B3:B31.
- Press and hold CTRL.
- Select cell range D3:D13.
- Go to tab "Insert" on the ribbon.
- Press with left mouse button on the "Insert Line or Area chart" button, and a pop-up menu appears.
- Press with left mouse button on the "Line with Markers" button, see the image above.
- A new chart appears on the worksheet, see the image below.
Double press with left mouse button on the chart to open the "Format Chart Area Pane".
Select the line on the chart, press with left mouse button on the checkbox "Smoothed Line" on the "Format Chart Area Pane".
Double-press with left mouse button on the y-axis values, the "Format Axis Pane" shows up.
Press with mouse on the radio button "Axis value:" and type -1.5 (Horizontal Axis crosses)
Press with right mouse button on on x-axis values. Press with mouse on "Add Major gridlines
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6. How to change the cosine wave amplitude
The general form of the COSINE wave is y = A*COS(B*(x-C))+D
Constant A in the formula above changes the amplitude or height of the cosine wave. The image above shows two different cosine waves, a green and a yellow one.
The yellow cosine wave has an amplitude or height of 2 and the green one has an amplitude of 1.
Formula in cell D14:
=COS(B3)
Formula in cell E14:
=2*COS(B3)
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7. How to change the cosine wave period
The general form of the cosine wave is y = A*COS(B*(x-C))+D
Constant B changes the period, the chart above shows two cosine waves. The green cosine wave completes a cycle in 2π or 360°, however, the yellow cosine wave completes two cycles in 2π or 360°.
Formula in cell C3:
=COS(B3)
Formula in cell D3:
=COS(2*B3)
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8. How to change the cosine wave midline
The general form of the Sin wave is y = A*Sin(B*(x-C))+D
Constant D lets you change the midline which is the centerline in which the cosine wave oscillates back and forth. The midline is horizontal and is right in between the minimum and maximum cosine function values.
Formula in cell D14:
=COS(B3)
The green cosine wave in column D has a maximum value of 1 and a minimum value of -1, the midline is 0 (zero).
Formula in cell E14:
=COS(B3)+1
The yellow cosine wave in column E has a maximum value of 2 and a minimum value of 0, the midline is 1 (zero).
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9. How to use the COS function with a right or right-angled triangle
A, B and C are angles, C is 90°, shown in the image above. A + B + C = 180°. One of the angles must be 90° (right angle triangle), in the example above C is 90°.
d, e, and f are lengths of the sides of the triangle. Side d and e are perpendicular to each other, meaning the angle between them are 90°.
COSINE A = e/f
COSINE A is equal to the ratio between sides e and f, this is only true if the triangle is a right-angled triangle.
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Functions in this article
Functions in 'Math and trigonometry' category
The COS function function is one of many functions in the 'Math and trigonometry' category.
Converts negative numbers to positive numbers.
Calculates the arccosine, or inverse cosine, of a number.
Calculates the inverse hyperbolic cosine of a number.
Calculates the inverse cotangent of a number.
Calculates the inverse hyperbolic cotangent of a number.
Perform different specific functions to a list or database.
Calculates the arcsine of a number.
Calculates the inverse hyperbolic sine of a number.
Calculates the arctangent of a number.
Calculates the arctangent of an angle using specific x- and y-coordinates.
Calculates the inverse hyperbolic tangent of a number.
Converts a number into a text representation with a given radix (base).
Rounds a number up to its nearest multiple.
Returns the number of combinations for a specific number of elements out of a larger group.
Calculates the number of combinations for a given number of elements from a larger group of elements.
Calculates the cosine of an angle.
Calculates the hyperbolic cosine of a number.
Calculates the cotangent of an angle specified in radians.
Calculates the hyperbolic cotangent of a hyperbolic angle.
Calculates the cosecant of an angle (radians).
Converts a text representation of a number in a given base into a decimal number.
Calculates degrees from radians.
Rounds a number up to the nearest even whole number.
Returns e raised to the power of a number, e equals 2.71828182845904.
Returns the factorial of a number.
Returns the double factorial of a number.
Rounds a number to the specified number of decimals, formats the number in decimal format using a period and commas, and returns the result as text.
Rounds a number down to the nearest integer or to the nearest multiple of significance.
Rounds a number down to the nearest integer or nearest multiple of significance.
Calculates the greatest common divisor that divides all given arguments without a remainder.
Removes the decimal part from positive numbers and returns the whole number (integer) except negative values are rounded down to the nearest integer.
Calculates the least common multiple. The least common multiple is the smallest positive integer that is a multiple of all integer arguments. Use the LCM function to find fractions with different denominators.
Lets you name intermediate calculation results which can shorten formulas considerably and improve performance.
Calculates the natural logarithm of a number. Natural logarithms are based on the constant e.
Calculates the logarithm of a number to a specific base.
Calculates the logarithm of a number using the base 10.
Calculates the inverse matrix for a given array.
Calculates the matrix product of two arrays, an array as the same number of rows as array1 and columns as array2.
Returns the remainder after a number is divided by divisor.
Calculates a number rounded to a given multiple.
Calculates the ratio of the factorial of a sum of values to the product of factorials.
Calculates the identity matrix for a given dimension
Returns the number pi (¶).
Calculates a number raised to a power.
Returns the product of the numbers given in the argument.
Returns the integer portion of a division.
Converts degrees to radians.
Calculates a random real number greater than or equal to 0 and less than 1.
Creates an array of random numbers
Returns a random whole number between the numbers you specify.
Rounds a number based on the number of digits you specify.
Rounds a number down based on the number of digits to which you want to round the number.
Calculates a number rounded up based on the number of digits to which you want to round the number.
Calculates the secant of an angle.
Calculates the hyperbolic secant of an angle.
Creates a list of sequential numbers.
Calculates the sum of a power series based on a formula.
Returns the sign of a number. 1 for a positiv number, 0 (zero) for a 0 (zero) and -1 for a negative number.
Calculates the sine of an angle.
Calculates the hyperbolic sine of a number.
Calculates the positive square root.
Returns a subtotal from a list or database, you can choose from a variety of arguments that determine what you want the function to do.
Allows you to add numerical values, the function returns the sum in the cell it is entered in. The SUM function is cleverly designed to ignore text and boolean values, adding only numbers.
Sums numerical values based on a condition.
Adds numbers based on criteria.
Calculates the product of corresponding values and then returns the sum of each multiplication.
Calculates the sum of the squares of the arguments.
Calculates the sum of the difference of squares of corresponding values in two arrays.
Calculates the sum of the sum of squares of corresponding values in two arrays.
Calculates the sum of squares of differences of corresponding values in two arrays.
Calculates the tangent of an angle.
Calculates the hyperbolic tangent of a number.
Removes the fractional part of the number to an integer.
Excel function categories
Excel functions that let you resize, combine, and shape arrays.
Functions for backward compatibility with earlier Excel versions. Compatibility functions are replaced with newer functions with improved accuracy. Use the new functions if compatibility isn't required.
Perform basic operations to a database-like structure.
Functions that let you perform calculations to Excel date and time values.
Let's you manipulate binary numbers, convert values between different numeral systems, and calculate imaginary numbers.
Calculate present value, interest, accumulated interest, principal, accumulated principal, depreciation, payment, price, growth, yield for securities, and other financial calculations.
Functions that let you get information from a cell, formatting, formula, worksheet, workbook, filepath, and other entitites.
Functions that let you return and manipulate logical values, and also control formula calculations based on logical expressions.
These functions let you sort, lookup, get external data like stock quotes, filter values based a condition or criteria, and get the relative position of a given value in a specific cell range. They also let you calculate row, column, and other properties of cell references.
You will find functions in this category that calculates random values, round numerical values, create sequential numbers, trigonometry, and more.
Calculate distributions, binomial distributions, exponential distribution, probabilities, variance, covariance, confidence interval, frequency, geometric mean, standard deviation, average, median, and other statistical metrics.
Functions that let you manipulate text values, substitute strings, find string in value, extract a substring in a string, convert characters to ANSI code among other functions.
Get data from the internet, extract data from an XML string and more.
Excel categories
Latest updated articles.
More than 300 Excel functions with detailed information including syntax, arguments, return values, and examples for most of the functions used in Excel formulas.
More than 1300 formulas organized in subcategories.
Excel Tables simplifies your work with data, adding or removing data, filtering, totals, sorting, enhance readability using cell formatting, cell references, formulas, and more.
Allows you to filter data based on selected value , a given text, or other criteria. It also lets you filter existing data or move filtered values to a new location.
Lets you control what a user can type into a cell. It allows you to specifiy conditions and show a custom message if entered data is not valid.
Lets the user work more efficiently by showing a list that the user can select a value from. This lets you control what is shown in the list and is faster than typing into a cell.
Lets you name one or more cells, this makes it easier to find cells using the Name box, read and understand formulas containing names instead of cell references.
The Excel Solver is a free add-in that uses objective cells, constraints based on formulas on a worksheet to perform what-if analysis and other decision problems like permutations and combinations.
An Excel feature that lets you visualize data in a graph.
Format cells or cell values based a condition or criteria, there a multiple built-in Conditional Formatting tools you can use or use a custom-made conditional formatting formula.
Lets you quickly summarize vast amounts of data in a very user-friendly way. This powerful Excel feature lets you then analyze, organize and categorize important data efficiently.
VBA stands for Visual Basic for Applications and is a computer programming language developed by Microsoft, it allows you to automate time-consuming tasks and create custom functions.
A program or subroutine built in VBA that anyone can create. Use the macro-recorder to quickly create your own VBA macros.
UDF stands for User Defined Functions and is custom built functions anyone can create.
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