Answer to Question #99744 in Mechanics | Relativity for AbdulRehman

Question

Try evaluating the numerator and denominator separately.]
(c) Sketch a graph of cosh θ vs. θ, letting θ range from large negative
values to large positive values. [Hint: Note that for large positive θ,
e
−θ
is very small (e
−θ ≈ 0).]
(d) Sketch a graph of sinh θ vs. θ, letting θ range from large negative
values to large positive values. [Hint: Note that for large positive θ,
e
−θ
is very small (e
−θ ≈ 0).]
(e) Sketch a graph of v/c vs. θ for v/c = tanh θ, letting θ range from
large negative values to large positive values. [Hint: Note that for
large positive θ, e
−θ
is very small (e
−θ ≈ 0).]
(f) Let τ = 1sec and let θ range from large negative values to large
positive values. Sketch the curve in spacetime described by:
t = τ cosh θ,
x = (cτ) sinh θ.
(g) Let d = 1Ls and let θ range from large negative values to large
positive values. Sketch the curve in spacetime described by:
t = (d/c) sinh θ,
x = d cosh θ.

Answer 1

c) The graph of the function is shown below for large negative theta to large positive theta:

$$y(\theta)=\text{cosh}\theta$$

d) Below is the graph for

$$y(\theta)=\text{sinh}\theta:$$

e) Below we can see the graph of

$$y(\theta)=\text{tanh}\theta:$$

f) The following are the graphs of the two functions:

$$y(\theta)=\tau\text{cosh}\theta=\text{cosh}\theta\space\text{(red)},\\ g(\theta)=c\tau\space\text{sinh}\theta=3\cdot10^8\cdot\text{sinh}\theta\space \text{(green)}:$$

g) Finally, show the graphs

$$y(\theta)=\frac{d}{c}\text{sinh}\theta=\text{sinh}\theta\space\text{(red)},\\ g(\theta)=d\space\text{cosh}\theta=3\cdot10^8\cdot\text{cosh}\theta\space \text{(green)}:$$