Question

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

Answer 1

ANSWER

$- \frac{\pi}{4}$

EXPLANATION

The given function is,

$f(t) = 2 \csc(t + \frac{\pi}{4} ) - 1$

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,

$f(t) = 2 \csc(t + \frac{\pi}{4} ) - 1$
There has been a horizontal shift of
$\frac{\pi}{4}$
to the left.

The transformed function will have a sample period,

$[ - \frac{\pi}{4} , \frac{7\pi}{4} ]$

Therefore a sample period begins at

$- \frac{\pi}{4}$