# Hyperbolic Sine

Hi everyone,

I was in the middle of solving a physics problem and came across a math term I am having trouble solving. It is the hyperbolic sine term in this equation:

$$T=\frac{2.0x10^{-8}}{sinh^{2}[\frac{\sqrt{130(2.6x10^{10}-130)}}{1.05x10^{-34}}6x10^{11}]+2.0x10^{-8}}$$

When plugging the sinh term into the calculator, I receive an error due to the massive size of the solution. Is there an equivalent method of taking a hyperbolic sine that can be done by hand since the calulator cannot handle the large exponent?

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For the low road, get yourself a copy of the CRC Standard Math Tables. It has tables for Hyperbolic Functions.

For the high road there is Mathematica (my favorite) or MatLab.

For myself, even though I have copies of Mathematica and Matlab (both) at my easy disposal, I still like my book of standard math tables at times.

Last edited:
arildno
Homework Helper
Gold Member
Dearly Missed
Why bother?

HypSine(Humungous) equals 1/2*e^Humungous.

And 1/Superbig is just about zero.

Thanks for the replies. I suppose I will just use Mathematica this evening to obtain some number besides zero since it's a probability. Basically, it is the likelihood of a human launching from the Earth's surface at 4 m/s and reaching Jupiter.

Tell use what the odds are. OK?

HallsofIvy
Homework Helper
Xkaliber said:
Thanks for the replies. I suppose I will just use Mathematica this evening to obtain some number besides zero since it's a probability. Basically, it is the likelihood of a human launching from the Earth's surface at 4 m/s and reaching Jupiter.
Why would you want an answer "besides zero"? Since 4 m/s is well below escape speed from earth, the "probabilty" of reaching Jupiter (or any thing except earth itself) is zero.

Well, quantum mechanically the probability is not exacly zero. Through the process known as "tunneling", a particle or object can travel through a potential energy barrier, in this case gravity, with its total energy less than the potential energy. I did actually put zero as my final answer in the end since I included my steps for solving the problem. The final probability ended up being something along the lines of $$e^{10^{44}}$$

arildno
Homework Helper
Gold Member
Dearly Missed
I think you forgot a minus sign somewhere in your exponent.

Office_Shredder
Staff Emeritus
Gold Member
Actually, thanks to the many worlds variety of quantum mechanics there are $$e^{10^{5000}}$$ ways of a person launching from earth at 4 m/s. So $$e^{10^{44}}$$ people actually escape earth for each person that attempts to launch.

*nod*

HallsofIvy
Homework Helper
Office_Shredder said:
Actually, thanks to the many worlds variety of quantum mechanics there are $$e^{10^{5000}}$$ ways of a person launching from earth at 4 m/s. So $$e^{10^{44}}$$ people actually escape earth for each person that attempts to launch.

*nod*
Are you sure there shouldn't be a negative sign in the exponent? If not, I jump up and down a few times and Jupiter is overrun with people!

Office_Shredder
Staff Emeritus