Question

Identify the beginning of a sample period for the function: : f(t)=2csc(t+pi/4)-1

Answer 1

ANSWER


`- (\pi)/(4)`

Step-by-step explanation

The given function is,


`f(t) = 2 \csc(t + (\pi)/(4) ) - 1`

This function has a period of

`2\pi`
just as the parent function


`f(t) = \csc(t )`

A sample period of this parent function is


`[ 0 , 2\pi]`

Which begins at zero.

For the transformed function,


`f(t) = 2 \csc(t + (\pi)/(4) ) - 1`
There has been a horizontal shift of

`(\pi)/(4)`
to the left.

The transformed function will have a sample period,


`[ - (\pi)/(4) , (7\pi)/(4) ]`

Therefore a sample period begins at


`- (\pi)/(4)`