Answer:
[tex]y=3sec\left(\frac{1}{2}x\right)[/tex]
Step-by-step explanation:
The graphs of [tex]sec(x)[/tex] can be obtained from the graph of the cosine function using the reciprocal identity, so:
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
But in this problem, the graph stands for the function:
[tex]y=3sec\left(\frac{1}{2}x\right)[/tex]
Because the period is now 4π as indicated and for [tex]x=0[/tex] in the figure and this can be proven as follows:
[tex]Period=\frac{2\pi}{\frac{1}{2}}=4\pi[/tex]
Also, [tex]for \ x=1 \ then \ y=3[/tex] as indicated in the figure and this can be proven as:
[tex]y=3sec\left(\frac{1}{2}x\right) \\ \\ y=\frac{3}{cos(0.5x)} \\ \\ y=\frac{3}{cos(0.5(0))} \\ \\ y=\frac{3}{1}=3[/tex]
