Hyperbolic Sine - Exponent transition

Thread starter porcupineman23
Start date Feb 12, 2014
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Exponent Hyperbolic Sine Transition

In summary, the hyperbolic sine function, defined as sinh(x) = (e^x - e^-x)/2, is a special case of the exponential function with an imaginary input value. It has a range of values from -∞ to +∞ and its graph is stretched along the x-axis compared to the regular sine graph. Some real-life applications of hyperbolic sine include modeling oscillating systems, calculating trajectories, analyzing financial data, and signal and image processing.

Feb 12, 2014

porcupineman23

Hey
I didn't understand the transition below,
I'd be glad for some help
thanks

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Feb 12, 2014

AlephZero

Science Advisor

Homework Helper

Multiply all the terms by ##e^{ih\omega/2}##.
Then multiply all the terms by -1.

Feb 12, 2014

porcupineman23

Thanks !

1. What is the formula for calculating hyperbolic sine?

The formula for calculating hyperbolic sine is sinh(x) = (e^x - e^-x)/2, where e is the base of the natural logarithm and x is the input value.

2. How is the hyperbolic sine function related to the exponential function?

The hyperbolic sine function is a special case of the exponential function, where the input value is imaginary. It is defined as sinh(x) = (e^x - e^-x)/2, while the exponential function is defined as e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...

3. What is the range of values for hyperbolic sine?

The range of values for hyperbolic sine is from -∞ to +∞. This means that the function can output any real number as long as the input value is also a real number.

4. How is the graph of hyperbolic sine different from the graph of regular sine?

The graph of hyperbolic sine has a similar shape to the regular sine graph, but it is stretched along the x-axis. This is because the input values for hyperbolic sine are not limited to just real numbers like regular sine, but can also include imaginary numbers.

5. What are some real-life applications of hyperbolic sine?

Hyperbolic sine has various applications in fields such as engineering, physics, and economics. It is used to model oscillating systems, calculate the trajectories of projectiles, and analyze financial data. It is also used in signal processing and image processing to remove noise from data.