CSC in Google Sheets: Calculate Cosecant with Signed Angle Controls

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples use ordinary web-spreadsheet numeric cells; other clients and imported files are not separately certified.
• Checked: October 14, 2026; official CSC reference. Documentation and independent calculations, without native Sheets execution.

=CSC(angle)

The required argument is an angle in radians. For degrees, convert the input with PI()/180. Cosecant is 1/SIN(angle); it does not return the inverse-sine angle and is not interchangeable with ASIN.

Use explicit units in the source heading. A numeric result can be plausible even when a degree value was passed directly as radians, so error handling alone does not diagnose that mistake.

Enter 15, 30, 60, 90, 210 degrees in A2:A6. Fill =CSC(A2*PI()/180) down. Expected values are approximately 3.863703305, 2, 1.154700538, 1, −2.

The negative result at 210 degrees follows the negative sine there. Removing the sign changes the question to magnitude only. Cosecant’s real magnitude is at least one wherever the ratio is defined; this mathematical bound is separate from native extreme-value behavior.

In a specified acute right triangle, let the opposite side be 6 and the angle 25 degrees:

=6*CSC(25*PI()/180)

Expected hypotenuse: approximately 14.197209499. Multiplying the unrounded result by SIN of the same angle reconstructs approximately 6.

The side’s role is essential. If six described an adjacent side instead, SEC would express the corresponding relationship. The function cannot infer the geometry from a number alone.

For a 30-degree angle, =1/SIN(30*PI()/180) gives 2. For a supplied sine ratio 0.5, =ASIN(0.5)*180/PI() gives 30 degrees. ASIN and CSC therefore take and return different kinds of quantities.

Keep ratio, radian and degree columns distinct. In a nested formula, check which quantity each inner expression actually produces before feeding it to the next function.

At 60 degrees, =CSC(PI()/3)^2-COT(PI()/3)^2 is expected to give approximately 1. The individual squared values are 4/3 and 1/3. COT shares sine in its denominator.

This ordinary-input identity is not a stable verification method near all singularities. Large squared terms can be nearly equal, and subtracting them can amplify numerical loss.

Google’s zero example pins the literal CSC(0) error. Its sample usage also mentions CSC(PI()), but that mention alone is not a numerical-accuracy guarantee at the mathematical singularity pi.

At other integer multiples of pi, the ideal ratio is undefined, while a finite PI approximation can leave a small denominator and a huge result. Keep this distinction visible rather than asserting that every constructed singular input returns the same native code.

The page does not supply an exhaustive type or magnitude matrix. Use the small signed controls and test any precision-critical source range in the target spreadsheet.

• Google CSC help.
• Editorial testing standards.

Inputs are fictional. Approximate numerical answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Complete coercion, extreme-magnitude and cross-client behavior remain untested.