Question

What is the period of the function y=tan(pi/4(x-pi/3))

Answer 1

Explanation:

The answer is 4

Answer 2

We need to calculate the period of the function

`y=tan((\pi)/(4)(x-(\pi)/(3)))`

Periodicity of a general function is given as follows:

`a * tan (bx\mp c)\mp d=(tan(peridocity))/(\left | b \right |)`

Now, periodicity of
`tan(x)` is
`\pi`.

Now,

Periodicity of the function:

`y=tan((\pi)/(4)(x-(\pi)/(3)))` is given by:

`y=tan((\pi)/(4)(x-(\pi)/(3)))=tan ((\pi)/(4)x-(\pi^2)/(12))`

here,
`b=(\pi)/(4)`

`(\pi)/(|(\pi)/(4) |) =(4 * \pi)/(4) =\pi`

Therefore, the period of the function is 4.