Chapter 1, Problem 1.44P

To determine

(a)

When two frames differ only by rotation of x and the y axis through an angle θ, to become $x’$ and $y’$, then

  $\begin{array}{l}x\text{'}=x\cos \theta -y\sin \theta \\ y\text{'}=y\cos \theta +x\sin \theta \end{array}$

To determine

(b)

That the standard Lorentz transformation equations can be written as

  $\begin{array}{l}x\text{'}=x\cosh \varphi -ct\sinh \varphi \\ ct\text{'}=ct\cosh \varphi -x\sinh \varphi \end{array}$

Where, $\varphi ={\tanh }^{-1}\left(\frac{v}{c}\right)$ .