Question

METAL FOR HELP :

Answer 1

hint:
for question #1, we can write this:
\[\begin{gathered}
4\sec \left( {3t - 6\pi } \right) = \frac{4}{{\cos \left( {3t - 6\pi } \right)}} = \frac{4}{{\cos \left( {3t} \right)\cos \left( {6\pi } \right) + \sin \left( {3t} \right)\sin \left( {6\pi } \right)}} = \hfill \\
\hfill \\
= \frac{4}{{\cos \left( {3t} \right)\cos \left( {6\pi } \right) + \sin \left( {3t} \right)\sin \left( {6\pi } \right)}} = \frac{4}{{\cos \left( {3t} \right)}} = 4\sec \left( {3t} \right) \hfill \\
\end{gathered} \]

Answer 2

so, what can you conclude?

Answer 3

would it be pi

Answer 4

you have to note that the period of your function is T/3, where T is the period of cosec x function.

Answer 5

would I use DeMoivres theorem

Answer 6

I think that it is suffice to use the graph of sec x function, namely the subsequent graph: