IMSIN

What it does

IMSIN(inumber)

IMSIN(inumber) returns the complex sine. Real and imaginary coefficients use radians where a circular angle is involved. For pure imaginary bi, the mathematical result is i*sinh(b).

Try it

=IMSIN("i") gives about "1.1752011936438i". With zero real coordinate the real sine component vanishes, leaving i*sinh(1). =IMSIN("0") returns text zero.

Quirks

The input may be numeric or complex text with lowercase i or j; the result is complex text. The current parser rejects malformed text with #NUM! and the wrapper rejects logical values with #VALUE!.

The current circular helper has a real-coordinate magnitude boundary at 134217728. The imaginary coordinate instead feeds an exponential and its reciprocal. Large coordinates can fail in either leaf; replacing the pair with independent native sine and hyperbolic calls changes the implementation's rounding history.

How to implement

Parse the two coefficients and suffix before doing arithmetic; use the common complex formatter afterward. Retain suffix consistency, suppress a zero component and omit the coefficient one before the imaginary unit. Formatting and parsing have their own fifteen-significant-digit rules, so testing only the algebra misses observable behaviour.

For z=a+bi, the mathematical component formula is sin(a)*cosh(b) + i*cos(a)*sinh(b). The current sine/cosine route forms exp(b) using the worksheet exponential and a stored reciprocal for exp(-b), then forms the half-sum and half-difference. Independent sinh/cosh calls need not share that rounding history. The formula is a derivation aid; the named runtime leaves and stores in the current source define its implementation candidate. Validate text output as well as numeric components, and keep unmeasured rounding stages open.

Rust code

47 imsin "IMSIN" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| Ok(z.sin())) }

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

IMEXP expresses the exponential relation; IMCOS is a related circular function; COMPLEX constructs the input.

Named variants

No named variants are recorded yet.