A graph shows how one input changes another quantity across a coordinate system, including repeating or curved behavior.
Use it to see rate, shape, turning points, period, phase, or domain behavior rather than treating a result as a one-off number.
The relationship
Write the rule before calculating
sinh x = (eˣ−e⁻ˣ)/2; cosh x = (eˣ+e⁻ˣ)/2; reciprocal functions and real principal inverses follow from these definitions.
See the structure
What the calculation is doing
∿ ∿ ∿one period / curvesinh x = (eˣ−e⁻ˣ)/2; cosh x = (eˣ+e⁻ˣ)/2; reciprocal functions and real principal inverses follow from these definitions.
Worked interpretation
Read the result in context
sinh 0 = 0, cosh 0 = 1, and asinh 0 = 0.
Interpret with care
Important boundary
A graph’s scale, domain, period, and phase conventions matter; a drawn curve is not proof of global behavior.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Extended domain
Complex hyperbolic functions
Hyperbolic functions accept complex inputs and connect directly to exponential and ordinary trigonometric identities.
Try an example
COMPLEX RESULT0.634963914785 + 1.29845758142i
Principal branch
Quick guide
How to use this calculator
Enter the known values and choose degrees or radians where the page offers a unit selector.
Select the intended function, identity family, or solve direction when needed.
Read the primary answer first, then inspect domain notes, supporting values, or the graph.
Calculation method
Apply the selected trigonometric relationship
sinh x = (eˣ−e⁻ˣ)/2; cosh x = (eˣ+e⁻ˣ)/2; reciprocal functions and real principal inverses follow from these definitions.
The calculator validates real-function domains and reports undefined angles or impossible triangles explicitly instead of displaying NaN, Infinity, or a misleading zero.
Worked example
Worked example
sinh 0 = 0, cosh 0 = 1, and asinh 0 = 0.
sinh x = (eˣ−e⁻ˣ)/2; cosh x = (eˣ+e⁻ˣ)/2; reciprocal functions and real principal inverses follow from these definitions.
Supported inputs
Precision and limits
Angle units
Degree/radian selectors apply only to fields labelled as angles. Triangle-law angles are explicitly entered and returned in degrees. Sinusoidal model arguments are explicitly radians.
Numerical precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Exact-value pages return symbolic radical forms only for their stated standard-angle table.
Supported magnitude
Numeric inputs may be zero or have absolute magnitude from 1e-100 through 1e100. This bounded range prevents floating-point underflow and overflow from being shown as meaningful results.
Domains and branches
The primary panel preserves the familiar real-angle workflow. The extended panel evaluates principal complex branches in radians and plots the result; reciprocal singularities still return an explicit error.
Calculator-specific rule
The calculator enforces the real domain of every inverse function. Complex branch values are outside this page's scope.
