Solutions based on trial and error, inspection of numerical plots, etc., are not acceptable.

Consider the sinusoid:

$x(t)=$Acos$(t+),$ where $A>0$ and $in(-,].$ Time $t$ is in seconds. It is known that

$x(t)2\mathrm{.}4$ for exactly $18\%$ of each period;

it takes $0\mathrm{.}123$ seconds for the value of the sinusoid to drop from $2\mathrm{.}4$ to the next minimum $("$valley$")$;

the first zero of the sinusoid in positive time occurs at $t=0\mathrm{.}040($seconds$).$

Determine the amplitude $A.$

Determine the period and angular frequency $$ of $x(t).$

Determine the initial phase $$ of $x(t)$ as a fraction of $.($Two values are possible here.$)$

Write simple MATLAB code which computes and plots two periods of $|x(t)|($i$.$e$.,$ the absolute value of $x(t))$ starting at $t=0,$ using $150$ uniformly spaced samples per period $($i$.$e$.,$ a total of $300$ samples$).$ Upload your published MATLAB results $($code and figure$)$ to Canvas.