SIN in Google Sheets: Convert Degree Angles and Model a Cycle

• Introduced: original service launch date is not established by the official history reviewed; Sheets has no corresponding numbered desktop release in this guide.
• Availability: documented in the rolling Google Sheets service; examples use an ordinary web spreadsheet and numeric cells.
• Checked: October 14, 2026; official SIN reference. Documentation and independent calculations, without native Sheets execution or broader client certification.

=SIN(angle)

Google identifies the argument as a radian angle. Convert a degree value by multiplying it by PI()/180, or use RADIANS. A degree symbol in a cell format does not change the stored number into radians.

The output is a dimensionless sine ratio. Examples use English function names, comma separators and decimal points. Check the spreadsheet’s locale before pasting formulas with punctuation-sensitive numeric inputs.

Enter degrees −30, 0, 30, 90, 210 in A2:A6. Put Degree angle in A1 and Sine in B1. In B2 enter:

=SIN(A2*PI()/180)

Fill down. Expected outputs, within ordinary numerical precision, are −0.5, 0, 0.5, 1, −0.5. The signs follow the selected circular positions; equal negative results at −30 and 210 do not imply equal source angles.

For an explicit unit-error control, =SIN(30) is approximately −0.988031624. Its syntax is valid, so a formula-error check alone cannot detect that the intended unit was degrees.

For an illustrative vector with magnitude 18 and an angle of 30 degrees from the positive horizontal axis:

=18*SIN(30*PI()/180)

Expected vertical component: 9. Change the angle to −30 degrees and the expected component becomes −9. The sign is directional information, while the component’s unit matches the magnitude’s unit.

If the angle is measured from a different axis, state that convention before selecting SIN or COS. A correct trigonometric calculation can still describe the wrong geometry. COS supplies the horizontal component under the convention used here.

Define a fictional signal as baseline 20 plus amplitude 5 times the sine of a phase. The period is eight time units. Enter times 0, 2, 4, 6, 8 in D2:D6. In E2 enter and fill down:

=20+5*SIN(2*PI()*D2/8)

Expected values are approximately 20, 25, 20, 15, 20. Dividing time by eight creates a cycle fraction; multiplication by 2×pi converts cycles into radians. The formula already constructs a radian angle, so applying another degree conversion would be a mistake.

Keep the period, amplitude and baseline separately labelled in a reusable sheet. The chosen model does not prove that real observations follow a sinusoid. A fitted application would need its own assumptions and validation.

=ASIN(SIN(210*PI()/180))*180/PI()

Expected result: approximately −30 degrees, rather than 210. ASIN selects an angle in its principal range, and both angles share sine −0.5.

Retain the original phase if turn count or full-circle position matters. A one-value sine result has already discarded information that the inverse cannot recreate.

The mathematical result at a full half-turn is zero, but PI and trigonometric calculations use finite numerical representations. Treat a tiny residual with a justified comparison tolerance instead of declaring every nonzero stored digit a model failure.

Google’s page gives the radian definition, not an exhaustive numerical-limit or error table. Separate a unit mistake, an incorrectly chosen model and a precision question when reviewing an unexpected result. Use the small signed controls before copying a large range.

• Google SIN help.
• Editorial testing standards.

Worked inputs are fictional and outputs independently calculated. Approximate values are rounded mathematical expectations, not captured native results. Imported types, extreme magnitudes and a complete error/coercion matrix remain outside the tests.