Zoho Sheet CSC: Calculate reciprocal sine in radians

=CSC(angle)

Zoho documents an angle in radians and the identity CSC(angle) = 1/SIN(angle). Its examples include 0.3, −0.9 and 1/2 radians. The page says the input must be less than 2^27 and lists #NUM! for values greater than that threshold. Official CSC reference.

The function’s name refers to cosecant, not inverse sine. A reciprocal is 1/sin(x); an inverse trigonometric function answers which angle has a given sine. Do not substitute one for the other.

Enter numeric 30 in B2. In B3 enter =B2*PI()/180, then enter =CSC(B3) in B4. Independently, B3 represents π/6 and the expected result is 2.

The direct formula is:

=CSC(30*PI()/180)

The multiplication by π/180 is essential. =CSC(30) asks about 30 radians, not 30 degrees. Formatting the input cell with a degree symbol would not perform a numerical conversion.

As a separate check, =1/SIN(30*PI()/180) represents the same mathematical quantity. This identity check is independent reasoning; it is not a claim that either formula was executed in Zoho for this guide.

The first three agree with the rounded values printed by Zoho. Negative angles can produce negative values: sine is odd, so csc(-x) = -csc(x) where the reciprocal is defined. A value outside −1 to 1 is ordinary for cosecant; that interval restriction belongs to sine’s output, not its reciprocal.

The exact 1 and −2 entries are mathematical values at ideal angles. Floating-point representations of π and trigonometric calculations can produce tiny numerical differences, so do not infer an exact-bit guarantee or a universal accuracy bound from the table.

For a right-triangle model with an opposite side of 5 and an angle of 30 degrees, opposite/hypotenuse = sin(angle). Therefore the hypotenuse is 5*csc(angle) = 10.

A corresponding spreadsheet expression is =5*CSC(30*PI()/180). This example uses a dimensionless trigonometric ratio; the resulting length uses the same units as the input side. Converting degrees to radians changes the angle representation, not the length unit.

Near zero, sine is small, so its reciprocal is large. That makes small angle errors particularly important. For instance, a formula applied to an angle rounded to zero may become undefined even when the intended nonzero angle had a finite, very large result. Retain input precision and inspect the source measurement rather than merely increasing displayed decimal places.

Mathematically, cosecant is undefined when sine is zero, including zero and integer multiples of π. Avoid those exact singularities in a calculation that expects a finite value. The cited article does not establish the exact Zoho error code at zero or whether a floating-point expression such as PI() is recognized as a singular angle, so those runtime claims are not made here.

The documented threshold wording also leaves equality and the treatment of very large negative magnitudes unclear. Use ordinary finite angles well inside the stated limit rather than inferring a symmetric absolute-value bound. Invalid nonnumeric inputs are listed as #VALUE!. CSC error reference.

SIN is the direct sine function. CSCH is hyperbolic cosecant and has a different mathematical definition. SEC is reciprocal cosine. These are distinct functions, not alternative spellings.

Official help was checked October 18, 2026. Values are independent reciprocal-sine calculations and comparisons with printed vendor examples; no authored Zoho execution or screenshot is claimed. Introduction release, mobile parity and historical lifecycle are not established by the cited page.