# How do you find the amplitude and period of y= -csc (5(x-pi))?

Jul 14, 2018

As below.

#### Explanation:

Standard form of the cosecant function is

$A \csc \left(B x - C\right) + D$

$y = - \csc \left(5 x - 5 \pi\right)$

$A = - 1 , B = 5 , C = 5 \pi , D = 0$

Amplitude $= | A | =$ NONE for cosecant function.

Period $= \frac{2 \pi}{|} B | = \frac{2 \pi}{5}$

Phase Shift $= - \frac{C}{B} = - \frac{5 \pi}{5} = - 5 \pi$, $\textcolor{red}{5 \pi}$ to the LEFT

Vertical Shift $= D = 0$