# How do you find the amplitude, period and phase shift for y=sin(theta-180^circ)?

Jul 13, 2018

As below.

#### Explanation:

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

$\text{Given } y = \sin \left(\theta - {180}^{\circ}\right) = \sin \left(\theta - {\pi}^{c}\right)$

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

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

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

$\text{Phase Shift " = -C / B = -pi / 1 = -pi, " "color(crimson)( pi " to the LEFT}$

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

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