Scenario:

You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions. They have asked you to undertake a series of such evaluations.

Task $1$:

Note: You need to have your calculator in radians $($RAD$)$ mode for this task $($since the angles are given in radians $-$

i$.$e$.,\backslash (\backslash$pi $\backslash )$ is featured$).$

a$)$ A voltage waveform from a circuit under test, that you are displaying on an oscilloscope, looks as follows:

You know that the signal takes the following form:

$\backslash [$

v$=$V$\_\{$p$\}\backslash$sin $(2\backslash$pi f t$-\backslash$emptyset$)$

$\backslash ]$

Taking measurements from the oscilloscope display above, determine $\backslash ($ V$\_\{$p$\},$ f $\backslash ),$ and $\backslash (\backslash$emptyset $\backslash ),$ and insert those values into the above equation.

Now rearrange your new equation to make the time $\backslash ($ t $\backslash ),$ the subject of this formula and hence determine, to within $3$ decimal places, the first point in time when the voltage waveform has a magnitude of $5\mathrm{.}25$ volts.