Calculator Inputs
Use the controls below to graph transformed hyperbolic functions.
Example Data Table
Sample values for common base hyperbolic functions.
| x | sinh(x) | cosh(x) | tanh(x) |
|---|---|---|---|
| -2 | -3.626860 | 3.762196 | -0.964028 |
| -1 | -1.175201 | 1.543081 | -0.761594 |
| 0 | 0.000000 | 1.000000 | 0.000000 |
| 1 | 1.175201 | 1.543081 | 0.761594 |
| 2 | 3.626860 | 3.762196 | 0.964028 |
Formula Used
This calculator applies transformed hyperbolic functions using:
y = A × f(B(x − C)) + D
- A controls vertical scaling or reflection.
- B controls horizontal compression or stretching.
- C shifts the graph left or right.
- D shifts the graph up or down.
Base hyperbolic definitions:
- sinh(x) = (ex − e−x) / 2
- cosh(x) = (ex + e−x) / 2
- tanh(x) = sinh(x) / cosh(x)
- sech(x) = 1 / cosh(x)
- csch(x) = 1 / sinh(x)
- coth(x) = cosh(x) / sinh(x)
How to Use This Calculator
- Select the hyperbolic function you want to graph.
- Enter the starting x-value and ending x-value.
- Choose a step size for smoothness and detail.
- Set A, B, C, and D for graph transformations.
- Pick a decimal precision for displayed results.
- Press Plot Function to generate the graph and values.
- Review the summary, graph, and generated table.
- Use CSV or PDF buttons to save your results.
Frequently Asked Questions
1) What does this graphing calculator do?
It graphs transformed hyperbolic functions across a custom x-range. It also builds a values table, highlights undefined points, and provides downloadable reports.
2) Which functions can I plot here?
You can graph sinh, cosh, tanh, sech, csch, and coth. Each function supports scaling, shifting, range changes, and precision adjustments.
3) Why do some points appear undefined?
csch(x) and coth(x) are undefined when sinh(x) equals zero. That happens at x = 0 before transformations, so the graph may split near that input.
4) What does the horizontal factor change?
The horizontal factor compresses or stretches the graph along the x-axis. Negative values also reflect the graph across the vertical axis.
5) What is the benefit of adjusting precision?
Precision changes how many decimal places appear in the table, summary, and exports. Higher precision helps when comparing close values or checking calculations.
6) Why is cosh(x) always positive?
The base cosh function is built from positive exponential terms. It never drops below 1 before transformations, though scaling and shifting can move the plotted result.
7) Can I use negative ranges and decimal steps?
Yes. Negative x-values work normally, and decimal step sizes help create smoother plots. Smaller steps usually produce more detailed graphs.
8) When should I choose a smaller step size?
Choose a smaller step when the curve changes rapidly or when you need a smoother graph. Keep total points reasonable for faster processing.