# How do you find the period and amplitude for y= -4 sin((2x)/3)?

Aug 8, 2018

color(green)(Amplitude = 4, " Period " = 3pi

#### Explanation:

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

$\text{Given } y = - 4 \sin \left(\frac{2}{3} x\right)$

$A = - 4 , B = \frac{2}{3} , C = D = 0$

$A m p l i t u \mathrm{de} = | A | = | - 4 | = 4$

"Period ' = (2pi) / |B| = (2pi) / (2/3) = 3 pi

$\text{Phase Shift } = \left(- \frac{C}{B}\right) = 0$

$\text{Vertical Shift } = D = 0$

graph{-4 sin(2/3 x) [-10, 10, -5, 5]}