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CSC Function (LibreOffice Calc)

Mathematics Beginner LibreOffice Calc LibreOffice 3.0

The CSC function returns the cosecant of an angle given in radians. It is the reciprocal of the sine function and is used in trigonometry, geometry, engineering, and waveform analysis.

The **CSC** function returns the **cosecant** of an angle measured in radians. It is defined as the reciprocal of the sine function:
**CSC(x) = 1 / SIN(x)**

What the CSC Function Does

  • Computes the cosecant of an angle
  • Angle must be in radians
  • Returns a real number or an error if undefined
  • Useful in trigonometry, geometry, physics, and engineering

Syntax

CSC(number)

Arguments

  • number:
    Angle in radians for which to compute the cosecant.

Basic Examples

Cosecant of 30° (converted to radians)

=CSC(RADIANS(30))
→ 2

Cosecant of π/2

=CSC(PI()/2)
→ 1

Cosecant of 45°

=CSC(RADIANS(45))
→ 1.414213562

Advanced Examples

Reciprocal identity

=1 / SIN(A1)

Use with DEGREES and RADIANS

=CSC(RADIANS(A1))

Engineering waveform example

=CSC(2 * PI() * frequency * time)

Avoid undefined values

=IF(SIN(A1)=0; "Undefined"; CSC(A1))

Parametric geometry

=CSC(theta) * radius

Edge Cases and Behavior Details

CSC returns a real number unless undefined

Undefined when:

  • SIN(number) = 0
    (e.g., 0, π, 2π, …)

Result → Err:532 (Division by zero)

Behavior details

  • Input must be in radians
  • Use RADIANS() for degree input
  • Very small sine values produce large magnitude results
  • Errors propagate

Common Errors and Fixes

Err:532 — Division by zero

Cause:

  • Angle corresponds to a sine of zero

Fix:

  • Check with IF(SIN(x)=0; ...)
  • Convert degrees properly

Unexpected output

Cause:

  • Input given in degrees instead of radians

Fix:

  • Wrap with RADIANS()

Best Practices

  • Always convert degrees to radians
  • Validate angles to avoid undefined values
  • Use CSC for reciprocal trigonometric modeling
  • Combine with SIN, COS, TAN for full trig workflows
  • Use in engineering formulas involving waveforms and oscillations
CSC is simply 1 ÷ SIN(x) — but using the dedicated function keeps formulas cleaner, more readable, and easier to audit.
  • SIN — sine
  • COS — cosine
  • TAN — tangent
  • SEC / COT / CSC — reciprocal trig functions
  • CSCH — hyperbolic cosecant
  • RADIANS / DEGREES — angle conversion

By mastering CSC, you can build clean, accurate trigonometric and engineering models in LibreOffice Calc.