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## Homework Statement

A space station observes a high-speed rocket passing by at speed β c in the +x direction. The rocket suddenly emits a light ray from a powerful laser. According to the space station, the light ray was emitted at an angle of θ with respect to the +x-axis. However, the technician aboard the rocket ship who fired the light pulse sent it off at an angle of θ′ with respect to the +x′-axis. (As usual, the x′-axis is chosen to be parallel to the x-axis.) Show that the angles are related by the formula

[tex] cos(\theta^\prime)= \frac {cos(\theta) - \beta}{1- \beta cos(\theta)}[/tex]

## Homework Equations

Lorentz Transforms

## The Attempt at a Solution

I'm having issues as soon as I start. If the velocity is ##\beta c## then wouldn't

[tex] cos(\theta)= \frac {\beta c}{c}=\beta[/tex]

Meaning the numerator of the given equation will always be zero?

Clearly this can't be the case but I fail to understand why it's not.

I assume I need to apply the transforms to the problem first and maybe one of the cosines or betas was suppose to be primed or something. My attempts so far are not working at all.

[tex] v_y=\frac{c sin(\theta)}{1-\frac{\beta c}{c^2}} [/tex]

Trying the same for v

_{x}just gives me c since the betas cancel. Really at a loss for this now.

Thanks for the help.