# How do you graph y=4-sin3(x-pi/3)?

Aug 3, 2018

As below.

#### Explanation:

Standard form of a sine function is $y = A \sin \left(B x - C\right) + D$

Given : $y = - \sin \left(3 x - \frac{3 \pi}{3}\right) + 4$

$A = - 1 , B = 3 , C = \pi , D = 4$

$A m p l i t u \mathrm{de} = | A | = | - 1 | = 1$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{3}$

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

$\text{Vertical Shift } = D = 4$

graph{- sin(3x - pi) + 4 [-10, 10, -5, 5]}