Respuesta :
We need to calculate the period of the function
[tex]y=tan(\frac{\pi}{4}(x-\frac{\pi}{3}))[/tex]
Periodicity of a general function is given as follows:
[tex]a \times tan (bx\mp c)\mp d=\frac{tan(peridocity)}{\left | b \right |}[/tex]
Now, periodicity of [tex]tan(x)[/tex] is [tex]\pi[/tex].
Now,
Periodicity of the function:
[tex]y=tan(\frac{\pi}{4}(x-\frac{\pi}{3}))[/tex] is given by:
[tex]y=tan(\frac{\pi}{4}(x-\frac{\pi}{3}))=tan (\frac{\pi}{4}x-\frac{\pi^2}{12})[/tex]
here, [tex]b=\frac{\pi}{4}[/tex]
[tex]\frac{\pi}{|\frac{\pi}{4} |} =\frac{4 \times \pi}{4} =\pi[/tex]
Therefore, the period of the function is 4.
