SINH in WPS Spreadsheet: Calculate Hyperbolic Sine from Real Inputs

• Introduced: documented by 2019-06-21 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
• Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=SINH(number)

The WPS lesson accepts a real-number argument and displays the definition (e^x−e^(−x))/2 in its formula image. That image was checked directly alongside the written lesson.

The input is a real parameter; it is not automatically a degree angle needing conversion. Although the name resembles SIN, applying PI()/180 without a reason from the underlying model changes the parameter and the result.

Enter −1, 0, 0.5, 1 and 2 in A2:A6. In B2 enter =SINH(A2) and fill down.

Expected values are approximately −1.175201194, 0, 0.521095305, 1.175201194 and 3.626860408. Negating the real parameter negates its hyperbolic sine; zero gives zero in the documented mathematical definition.

The output is not restricted to −1 through 1. In particular, the value at two is greater than three, which would be impossible for the ordinary real sine function.

For x=1:

=(EXP(1)-EXP(-1))/2

Expected result: approximately 1.175201194, agreeing with SINH(1). EXP supplies e raised to each real power.

This identity explains the function, but it is not a promise that a hand-written exponential subtraction is numerically superior to the built-in operation. For tiny parameters the subtraction involves nearly equal quantities, and very large parameters can create large intermediate values.

=SIN(1)
=SINH(1)

Independent expected results are approximately 0.841470985 and 1.175201194. The first treats one as a radian angle; the second applies the real hyperbolic definition.

Near zero they can appear similar. At 0.1, SINH is approximately 0.100166750, close to 0.1, but the difference grows with the input. A name similarity or one small-input comparison does not make the functions interchangeable.

Consider the explicit mathematical model L=2a*sinh(d/(2a)), with positive parameters a=5 and d=8. It can describe a symmetric catenary arc in an appropriate geometric model, but here it is simply a reproducible equation with stated inputs:

=2*5*SINH(8/(2*5))

Expected L: approximately 8.881059822 in the same length unit as a and d. The ratio d/(2a)=0.8 is dimensionless. Keep the factor outside SINH separate from the scaled parameter inside it.

If both a and d are doubled to 10 and 16, the ratio stays 0.8 and the expected L doubles to approximately 17.762119644. This is a scaling check on the equation, not a validated design for a cable, structure or physical installation.

For a known hyperbolic-sine value y=2, the mathematical inverse expression is:

=LN(2+SQRT(2^2+1))

Expected parameter: approximately 1.443635475. Applying SINH to that parameter has mathematical expectation 2. The LN and SQRT guides document the component operations.

This explicit expression is shown for a modest positive control. It is not promoted as a universally stable inverse implementation for every sign and extreme magnitude.

The walkthrough mentions #VALUE! for an argument that is not a real number, but it does not give a complete spreadsheet coercion matrix. This guide therefore does not infer the native handling of every numeric-looking string, blank, logical value or complex-text representation.

Check that the intended model is hyperbolic, that any scaling ratio has consistent units, and that the source is numeric. Current-build overflow limits and exact native precision have not been established by these independent calculations.

• WPS Academy: SINH lesson, 2019-06-21 (Chinese; Windows Personal scope).
• Editorial testing standards.

The direct WPS product lesson supports the stated function scope. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.