# How do you graph y = 2 + 1/2csc(x - 3pi/4)?

Mar 31, 2018

As below.

#### Explanation:

Standard form of equation : $y = A \csc \left(B x - C\right) + D$

Given equation is $y = \left(\frac{1}{2}\right) \csc \left(x - \left(\frac{3 \pi}{4}\right)\right) + 2$

$A m p l i t u \mathrm{de} = A = \frac{1}{2} = \text{ None for csc function}$

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

$\text{Phase Shift " = -C / B = (3pi)/4, " " (3pi)/4 " to the right}$

$\text{Vertical Shift } = D = 2$

graph{(1/2) csc (x - (3pi)/4) + 2 [-10, 10, -5, 5]}