CSC in Excel: Calculate Cosecant and Recover a Hypotenuse

• Introduced: Microsoft marks the function as introduced in Excel 2013. Version-marker reference.
• Availability: official help 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; official CSC reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=CSC(number)

The required number is a radian angle. Microsoft requires an absolute value below 2^27 and documents #NUM! outside that bound and #VALUE! for nonnumeric input. The direct reference also states the reciprocal relationship with SIN.

Convert degrees explicitly; CSC(30) means 30 radians. The result is a dimensionless ratio, not a returned angle and not an inverse-sine operation.

Enter 30, 45, 90, 150, 270 in A2:A6 and fill =CSC(A2*PI()/180) down in B2:B6. Expected outputs are approximately 2, 1.414213562, 1, 2, −1.

The 30- and 150-degree inputs have equal sine and therefore equal cosecant. The negative result at 270 degrees is directional information. Taking ABS would answer a magnitude-only question.

For a stated acute right triangle with opposite side 9 and angle 40 degrees:

=9*CSC(40*PI()/180)

Expected hypotenuse: approximately 14.001514442. Because cosecant is hypotenuse/opposite, the input length must be the opposite side, not the adjacent side.

Multiply the unrounded hypotenuse by SIN of the same radian angle to reconstruct approximately 9. That forward check catches a swapped side or a missing degree conversion without requiring an unrelated dataset.

At a 30-degree angle, =1/SIN(30*PI()/180) gives 2. By contrast, =ASIN(0.5)*180/PI() gives 30 degrees. ASIN recovers a principal angle from a sine ratio; CSC takes an angle and returns the reciprocal ratio.

The inputs and outputs have different meanings even though both operations involve sine. Column headings should say whether the cell holds degrees, radians or a ratio.

At 45 degrees, =CSC(PI()/4)^2-COT(PI()/4)^2 is expected to give approximately 1. The values are sqrt(2) and 1, so the squared difference is 2−1.

COT shares sine in its denominator. Near a zero of sine, both ratios become large and subtracting their squares can lose precision. This small identity check is not a stable validation method for all magnitudes.

Cosecant is mathematically undefined where sine is zero, including zero and integer multiples of pi. The source page does not explicitly give a complete singular-input native error table, so this guide distinguishes mathematical undefinedness from a verified display code.

For ordinary nonzero finite controls, =1/CSC(30*PI()/180) reconstructs sine 0.5. It does not identify which of the multiple possible source angles produced that sine.

Keep singular inputs visible and decide an explicit worksheet policy instead of replacing every large value with zero. Finite PI approximations, imported types and behavior at the documented magnitude boundary need target-workbook tests where they matter.

• Microsoft CSC reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.