SINH
Returns the hyperbolic sine of a number. Defined for all real numbers.
SINH(number)Arguments
numberAny real number for which to find the hyperbolic sine.
=SINH(0)SINH(0) is always 0
=SINH(1)Hyperbolic sine of 1
- •SINH(x) = (eˣ - e⁻ˣ) / 2
- •SINH is an odd function: SINH(-x) = -SINH(x)
- •Used in physics, engineering, and probability
- •Confusing SINH with SIN - SINH is the hyperbolic sine, unrelated to angles or the unit circle, while SIN is the regular trigonometric sine based on an angle in radians
- •Expecting the result to stay bounded like SIN's does - SINH grows without bound for large positive or negative inputs, unlike SIN which always stays between -1 and 1
- •Forgetting that SINH is an odd function, so a sign error in the input (using -x instead of x, or vice versa) simply flips the sign of the result rather than causing a larger discrepancy
ASINHPerforms the inverse operation - calculates the inverse hyperbolic sine, undoing what SINH calculates.COSHCalculates the hyperbolic cosine, a closely related function often used alongside SINH in the same formulas.SINCalculates the regular (non-hyperbolic) sine of an angle, a different function despite the similar name, with a bounded output between -1 and 1.What's the difference between SINH and SIN?
They're unrelated despite the similar name - SINH is the hyperbolic sine, unbounded and taking any real number as input, while SIN is the regular trigonometric sine, bounded between -1 and 1 and interpreting its input as an angle in radians.
Why did SINH return a huge number?
SINH grows exponentially for larger inputs since it's derived from exponential terms - even moderately large numbers can produce very large results.
What is SINH(0)?
Always 0 - this is a defining property of the hyperbolic sine function, since it's an odd function symmetric around the origin.
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