How do u write lorentz transformation in terms of hyperbolic functions i really don't know where to start.

Question

Lorentz transformation is
t= gamma(t' +(v/c^2)x')
x=gamma(x'+vt')
y=' and
z=z'.

i don't know how to show
ct=ct'cosh(theta) +x'sinh(theta)
x=ct'sinh(theta) +x'cosh(theta)

i'm really stuck to where to start

Answer 1

I see no one has answered this yet.

Have you looked at the page in the link below?

It gives some useful identities and you may be able to work from these to prove the equations given. First of all note the following identities -

cosh(theta) = gamma
tanh(theta) = beta = v/c

Starting with your first equation,

t = gamma(t' + (v/c^2)x') so
ct = c * gamma(t' + x' (v/c^2))
ct = ct' gamma + x' gamma (v/c)
ct = ct' cosh(theta) + x' cosh(theta) tanh(theta)
ct = ct' cosh(theta) + x' sinh(theta)

since sinh = cosh * tanh

I assume the second equation can be similarly transformed.

I hope this helps but I am a bit out of my depth here.

Answer 2

You won't get anywhere unless you know that
gamma = [1 - {v/c}(^2)](^-1/2).