Hyperbolic functions (1 Viewer)

NewiJapper · Mar 16, 2011

Solve the equation 2sinh(2x)-sinh(x)=0

I expanded using the double angle formula but then got no-where. Any halp?

hscishard · Mar 16, 2011

NewiJapper said:
Solve the equation 2sinh(2x)-sinh(x)=0

I expanded using the double angle formula but then got no-where. Any halp?

What's sinh? It's on the calc but i dunno what it does.
Anyway if it's really similar to sin

4sinxcosx - sinx = 0
sinx(4cosx-1)=0
sinx =0
cosx = 1/4

Drongoski · Mar 17, 2011

NewiJapper said:
Solve the equation 2sinh(2x)-sinh(x)=0

I expanded using the double angle formula but then got no-where. Any halp?

Is this a General Maths question?

2sinh2x - sinhx = 0

.: 2x2sinhxcoshx - sinh x = 0

.: sinhx(4coshx - 1) = 0

.: either sinhx = 0 ==> x = 0

or cosh x = 1/4 ==> x = cosh^-1 (1/4)

hscishard · Mar 17, 2011

I just realised the title of this thread.
I think hyperbolic functions are way too advanced for general maths. It sounds very complicated

Drongoski · Mar 17, 2011

hscishard said:
I just realised the title of this thread.
I think hyperbolic functions are way too advanced for general maths. It sounds very complicated

The hyperbolic functions in many ways look like and behave like the trig functions

$sinh x = \frac {e^x - e^{-x}}{2}$

$cosh x = \frac{e^x + e^{-x}}{2}$

$tanh x = \frac {sinh x} {cosh x} = \frac {e^x - e^{-x}}{e^x + e^{-x}}$

$cosh^2 x - sinh^2 x = 1$

$\frac {d}{dx} sinh x = cosh x$

$\int cosh x dx = sinh x + C$

$sinh2x = 2sinhx \cdot coshx$

$cosh2x = cosh^2 x+ sinh^2 x$

$sin \theta = \frac {e^{i \theta} - e^{-i \theta}}{2i}$

$cos \theta = \frac {e^{i \theta} + e^{-i \theta}} {2}$

$\therefore cis \theta = cos \theta + isin \theta = e^{i \theta}$

$\therefore (cis \theta )^n = (e^{i \theta })^n = e^{in \theta} = cis n \theta$ (De Moivre's Thm)

AAEldar · Mar 17, 2011

Pretty much what Drongoski said, however I don't think all of the trig results apply to hyperbolic functions (correct me if I'm wrong though).

If this is for school, why are you doing hyperbolic functions?

Drongoski · Mar 17, 2011

I think this is from NewiJapper's 1st Yr maths @ Newcastle Uni..

AAEldar · Mar 17, 2011

Drongoski said:
I think this is from NewiJapper's 1st Yr maths @ Newcastle Uni..

That would make sense, should probably check out the sig next time.

NewiJapper · Mar 17, 2011

I didn't know where to put it :/ it seemed at ext 1. And I got to your third line of working, but it looked weird for some reason so I wasn't sure

Drongoski · Mar 17, 2011

Whose work are you referring to and which 3rd line?

NewiJapper · Mar 17, 2011

Yours sorry. It's all good now though, thanks

Hyperbolic functions (1 Viewer)

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