COS in Excel: Calculate Components and Phase-Shifted Curves

• Introduced: original introduction release and first numeric build are not established by the official history reviewed.
• Availability: the official COS reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026. Documentation and independently calculated finite-value examples; no native Excel execution or broader platform certification.

=COS(number)

The required argument is an angle in radians. Microsoft documents conversion by multiplying degree values by PI()/180 or using RADIANS. The output is a dimensionless ratio; it is not a new angle.

Use English function names and your locale’s formula separator. Examples below use comma separators and decimal points. PI provides the conversion constant without typing a shortened approximation.

Enter degrees 0, 60, 90, 180, 360 in A2:A6. Put =COS(A2*PI()/180) in B2 and fill down. Expected outputs, allowing ordinary numerical approximation, are 1, 0.5, 0, −1, 1.

The first and last angles differ by a full turn but share the same cosine. If you need to track how many turns occurred, keep that information separately; COS is periodic and cannot retain it.

As a deliberate unit-error control, =COS(60) is approximately −0.952412980. The formula is using 60 radians. A cell containing 60 with a degree-sign display format still needs the explicit conversion.

For a vector of magnitude 20 at an angle of 60 degrees measured from the positive horizontal axis:

=20*COS(60*PI()/180)

Expected horizontal component: 10. At 120 degrees the same expression gives −10, showing that the vector points left in this coordinate convention.

The corresponding vertical component uses SIN. Keep both signs when reconstructing a direction. Taking absolute values may preserve component sizes while putting a vector in the wrong quadrant.

Suppose a model uses baseline 8, amplitude 2 and a phase offset of 60 degrees. Enter source phases 0, 60, 120, 180 in D2:D5. In E2 enter and fill down:

=8+2*COS((D2+60)*PI()/180)

Expected outputs are 9, 7, 6, 7. Parentheses ensure the source phase and offset are added before conversion to radians. Writing D2+60*PI()/180 would convert only the offset and mix incompatible units.

The minimum in this sampled table occurs when the total angle reaches 180 degrees. Changing a phase offset shifts where features occur; it does not change the amplitude from two or the baseline from eight. Label all model inputs so another reader can distinguish those roles.

=COS(-60*PI()/180)
=ACOS(COS(-60*PI()/180))*180/PI()

The first result is 0.5 and the second approximately 60. Cosine is even: +60 and −60 degrees have equal cosines. ACOS selects its nonnegative principal angle rather than recovering the original sign.

For an ordinary angle of 37 degrees, =SIN(37*PI()/180)^2+COS(37*PI()/180)^2 should be approximately 1. This identity is a useful mathematical control, not a proof that every stored floating-point result is exactly equal to one.

A nearly zero value at 90 degrees can reflect finite numerical representation. Inspect more decimal places and compare within a justified tolerance where appropriate. Do not round intermediate components unnecessarily if later calculations need their precision.

Check whether the angle is measured from the intended axis and whether a negative component is physically meaningful. Native extreme-angle accuracy, text coercion and all imported-workbook behaviors remain outside these independently computed examples.

• Microsoft COS reference.
• Editorial testing standards.

Numerical outputs are independent mathematical expectations, rounded where stated. Product-specific syntax and scope come from the cited reference. Native error/coercion matrices and extreme-value precision remain untested.