Visualize sinh, cosh, tanh and their inverses. Compare with circular trig functions and explore catenary curve applications.
Inspect how sinh, cosh, tanh, and their inverse functions behave over real inputs, then contrast their graphs with circular sine, cosine, and tangent. The explorer also connects cosh to the catenary shape used to model an ideal hanging cable. A common mistake is treating hyperbolic functions as ordinary trigonometric functions with a different label. Their names are related historically and through complex-number identities, but their real graphs, ranges, periodicity, and defining identities are different.
A concrete input and expected output from the current implementation.
Input
0 (with sinh selected)
Expected output
sinh(0) = 0
By definition, sinh(x) = (e^x - e^(-x)) / 2. At x = 0, both exponential terms equal 1, so their difference is 0.
For a real input x, the displayed hyperbolic values follow sinh(x) = (e^x - e^(-x)) / 2, cosh(x) = (e^x + e^(-x)) / 2, and tanh(x) = sinh(x) / cosh(x). Their graphs show that sinh is odd, cosh is even with a minimum of 1, and tanh approaches -1 and 1 without reaching either value.
The inverse graphs reverse the input-output relationship of the corresponding restricted functions. Asinh accepts every real input, acosh has real values only for inputs at least 1, and atanh has real values only between -1 and 1. The catenary view uses the cosh-based form y = a cosh(x / a), with positive a controlling the curve's scale and apparent sag.
No. Changing degrees to radians cannot turn cosine into hyperbolic cosine. For real x, cos(x) oscillates between -1 and 1, while cosh(x) is never below 1 and grows without bound in both horizontal directions. Their characteristic identities also differ: cosh(x)^2 - sinh(x)^2 = 1, whereas cos(x)^2 + sin(x)^2 = 1.
An inverse can accept only values produced by its original real function. Cosh produces values from 1 upward, so acosh(x) has no real result when x is below 1. Tanh produces values strictly between -1 and 1, so atanh(x) has no finite real result at or beyond those endpoints. Asinh has no comparable real-domain restriction.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.