COS Function in Apple Numbers: Cosine, Degree Conversion and Geometry

COS(radian-angle) returns the cosine of an angle expressed in radians. If a table stores degrees, convert them first: =COS(RADIANS(60)) has a mathematical result of 0.5.

This guide is based on Apple’s published function documentation and independently evaluated mathematical examples, not native Apple Numbers test output. Apple’s individual function documentation was consulted on 2026-10-11, using Formulas and Functions Help 15.4. That help version does not prove when the function first appeared in Numbers or whether an older iPhone, iPad, Mac or web release implements it identically. This guide deliberately separates Apple’s documented behaviour from independently calculated, mathematically expected values.

Apple documents COS(radian-angle) as cosine of a numeric radian angle, with examples COS(RADIANS(60)) = 0.5 and COS(PI()) = −1. This is useful in calculated tables because you can retain numerical expressions instead of storing a formatted text label. For input values, choose units explicitly; an angle of 30 degrees is not the same numeric angle as 30 radians. The worked table below is intentionally small, allowing every row to be checked before applying the formula to large datasets.

=COS(radian-angle)

The argument name and order above follow Apple’s official COS function reference. No optional parameters were documented for this function in the reviewed edition. A numeric argument can be a typed number, numeric expression, or reference to a cell containing a number according to Apple’s value-type definitions. Do not assume the application will convert text containing units or arbitrary imported strings to valid numeric input: that behaviour was not tested here.

Locale and formula punctuation: The formulas below show English-style decimal points (0.5) and use Apple’s standard function names. Apple says functions are case-insensitive and that hand-typed multi-argument formulas use a semicolon instead of a comma when the decimal symbol is a comma. The basic COS call has one argument, so its syntax does not need an argument delimiter. Nested formulas with multiple arguments still follow the user’s region. The documented rule appears in Functions overview; do not confuse it with CSV import/export delimiters.

Numbers table references: In a single table, B2 denotes B2 in that context; for another table, Numbers uses a qualified reference such as Angle Signals::B2. When typing a formula that pulls from a different table, select the intended cell and let Numbers construct the reference. Apple’s reference-type section documents the double-colon :: convention. A column name or a header may change how the editor displays an inserted reference.

Create a Numbers table called Angle Signals. Put degree values in B2:B8, with B1 labeled Degrees and C1 Cosine. Enter =COS(RADIANS(B2)) in C2 and fill through C8. Format column C as six decimal places and compare to the independently calculated values below. The use of RADIANS keeps the input unit unambiguous.

The table shows expected, rounded mathematical results. The accompanying evidence JSON stores independently computed underlying values and formula-by-formula checks. Minor last-digit differences in displayed decimals are possible across spreadsheet engines; none of the outputs above were observed in an Apple Numbers runtime.

A quick hand-entry check

Enter =COS(RADIANS(0)) in an unused cell and check whether a numerical result appears consistent with 1.000000 when formatted to six decimals. If your application reports an error or a noticeably different value, verify the function, data type, argument units, locale and table references before proceeding.

Project a length onto a horizontal direction

If B11 contains a line length of 10 and C11 contains an angle of 60 degrees above horizontal, =B11*COS(RADIANS(C11)) has an expected horizontal component of 5 length units. This is the adjacent/hypotenuse relationship; for the vertical component in the same convention use SIN instead.

Compare cosine and sine of complementary angles

=COS(RADIANS(60)) and =SIN(RADIANS(30)) are both mathematically 0.5. This is useful as a consistency check after transcribing data from a technical drawing. A result displayed as 0.500000 is a rounded presentation, not necessarily a claim that two internal floating-point computations are bit-for-bit equal.

Calculate a simple cycle offset

For a normalized cycle position in B12, =COS(2*PI()*B12) gives 1 at B12 = 0, approximately −1 at B12 = 0.5, and approximately 1 at B12 = 1. This creates a cosine pattern starting at its peak, unlike sine which starts at zero; it can serve as illustrative chart data, not a guaranteed model of any physical system.

• Degrees passed straight into COS: COS(60) means cosine of 60 radians, not cosine of 60 degrees; convert degree inputs with RADIANS.
• Assuming near-zero results are exactly stored zero: COS(PI()/2) is zero mathematically, but finite floating-point evaluation can produce a tiny nonzero value.
• Using SIN where the adjacent component is required: specify how the reference angle is measured before choosing a trigonometric function.
• Assuming ±π is an error threshold: Apple calls it the customary range only. The cosine function repeats for larger real inputs.
• Over-specified result precision: the six decimals in the examples are display rounding; they are not a native Numbers precision guarantee.
• Strings instead of numbers: verify cells actually contain numeric radians or degrees, not human-readable values suffixed with text.

What’s verified and what isn’t: Apple’s documentation supports the function definition, its argument types and the specific documented examples. The numeric table and advanced formula results are independently calculated mathematical expectations. We did not check an app-specific error-message spelling, text-to-number coercion, huge-input floating-point limit, first-supported Numbers version, or behaviour on every device. Errors or unexpected results on very old or locale-customized installations should be investigated with the current in-app Functions Browser.

Microsoft Excel documents COS(number) in radians and suggests RADIANS when the input is in degrees. For the real numeric examples here, the documented calculation is compatible with Numbers. Exact differences in error messages, coercion, import behavior and historical version support remain unverified; no Google Sheets-native test occurred.

The corresponding Microsoft Excel documentation was opened at Microsoft COS function on 2026-10-11. Apple and Microsoft share these familiar function spellings for the documented scalar inputs; that does not establish every edge case or feature’s version history. Google Sheets was not run and its 2026 function release coverage was not individually revalidated in this batch. Test imported models in the actual destination app rather than relying on common names alone.

• SIN — Apple official help (link opened and verified 2026-10-11)
• RADIANS — Apple official help (link opened and verified 2026-10-11)
• PI — Apple official help (link opened and verified 2026-10-11)
• DEGREES — Apple official help (link opened and verified 2026-10-11)

The links above point directly to Apple’s official function documentation. For a companion guide on this website, use the relevant function name in the Apple Numbers directory. These links do not imply that unverified cross-software behaviour has been tested.

• Apple Numbers — function documentation
• Apple’s value-type definitions
• Functions overview
• SIN — Apple official help
• RADIANS — Apple official help
• PI — Apple official help
• DEGREES — Apple official help

Verification status: Official documentation checked; example outcomes were independently reasoned or arithmetically checked where applicable. Not executed in Apple Numbers.

• No genuine Apple Numbers screenshots are included; this guide does not use mock application images.