SIN(radian-angle) returns the sine of an angle given in radians. If your data is measured in degrees, wrap the cell in RADIANS, for example =SIN(RADIANS(30)), whose mathematical result is 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 defines SIN(radian-angle) as sine of a numeric radian angle and documents SIN(RADIANS(30)) = 0.5 and SIN(PI()/2) = 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.

=SIN(radian-angle)

The argument name and order above follow Apple’s official SIN 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 SIN 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.

Make a table called Angle Signals. Enter B1 Degrees, C1 Sine, and put degree numbers into B2:B8 as shown. In C2 type =SIN(RADIANS(B2)), then fill down to C8. Display six decimals in column C; its values should lie between −1 and 1 for valid real-number inputs. The degree-to-radian step is deliberate and necessary.

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 =SIN(RADIANS(0)) in an unused cell and check whether a numerical result appears consistent with 0.000000 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.

Calculate the vertical rise of an angled line

Suppose B11 holds a segment length of 10 and C11 holds an angle of 30 degrees above the horizontal. =B11*SIN(RADIANS(C11)) gives a mathematically expected rise of 5 length units. If the angle is already in radians, use =B11*SIN(C11) instead. This is a geometric projection, not a substitute for checking real-world measurement accuracy.

Build a twelve-step periodic signal

Let B12 contain a period position of 3, and use =2*SIN(2*PI()*B12/12). It evaluates mathematically to 2 because B12 = 3 corresponds to one quarter of the cycle. Fill this formula alongside integer positions 0–12 to visualize a smooth periodic pattern in a chart. The denominator 12 controls the number of steps per cycle, while the leading 2 controls amplitude.

Diagnose a degree/radian mix-up

Compare =SIN(30) (sine of thirty radians) with =SIN(RADIANS(30)) (sine of thirty degrees). The latter is 0.5. The former is approximately −0.988032, a valid mathematical value but usually an unexpected answer in degree-based worksheets.

• No RADIANS conversion for degree input: SIN(30) is not 0.5; SIN(RADIANS(30)) is.
• Rounding floating-point output as a claim of exact zero: the sine of π is mathematically zero; numeric computation can produce a tiny residual. Format or compare using a tolerance where appropriate.
• Confusing sine and cosine: for a right triangle, sine is opposite/hypotenuse and cosine is adjacent/hypotenuse for a chosen angle. A mislabeled angle changes the interpretation.
• Degrees symbol stored as text: keep B cells numeric; a string such as 30° must be validated/converted before using the function.
• Mistaking ±π as the allowed domain: it is a common angle span, not a restriction on inputs. SIN is periodic for all real angles.
• Unexpected results on imported formulas: check that the source workbook used degrees or radians, and confirm table qualification if references cross tables.

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 SIN(number) using radians and recommends RADIANS for degree inputs. The main mathematical operation matches Numbers for the ordinary examples here. Google Sheets-native tests, historical feature support and exact formatting/error parity were not performed and should not be inferred from shared names.

The corresponding Microsoft Excel documentation was opened at Microsoft SIN 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.

• COS — 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
• COS — 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.