Problem $1$: Scientists use an instrument called an oscilloscope to visualize and measure electrical signals. These signals can come from devices that measure physical phenomena like sound and light waves. The data in Table $1$ represents extracted readings from an oscilloscope for a particular wave.

$\backslash$table$[[$Length$($angstrom$),$Amplitude$($volts$),$Length$($angstrom$),$Amplitude$($volts$)],[0\mathrm{.}0,-1\mathrm{.}65,1\mathrm{.}0,-1\mathrm{.}33],[0\mathrm{.}1,-0\mathrm{.}93,1\mathrm{.}1,-1\mathrm{.}87],[0\mathrm{.}2,0\mathrm{.}00,1\mathrm{.}2,-1\mathrm{.}99],[0\mathrm{.}3,0\mathrm{.}93,1\mathrm{.}3,-1\mathrm{.}65],[0\mathrm{.}4,1\mathrm{.}65,1\mathrm{.}4,-0\mathrm{.}93],[0\mathrm{.}5,1\mathrm{.}99,1\mathrm{.}5,0\mathrm{.}00],[0\mathrm{.}6,1\mathrm{.}87,1\mathrm{.}6,0\mathrm{.}93],[0\mathrm{.}7,1\mathrm{.}33,1\mathrm{.}7,1\mathrm{.}65],[0\mathrm{.}8,0\mathrm{.}48,1\mathrm{.}8,1\mathrm{.}99],[0\mathrm{.}9,-0\mathrm{.}48,1\mathrm{.}9,1\mathrm{.}87],[,]]$

Table $1$: Oscilloscope Readings for a Given Wave

Transform $($Given$,$ Find, Define Variables, Assumptions, Model$)$ the problem into a mathematical model. Demonstrate your calculations for amplitude, angular frequency, vertical and horizontal shifts. Report your trigonometric model for the given data.