# How do you determine the amplitude, period, and shifts to graph y = (1/2)sin(x - pi)?

Sep 8, 2016

Use the form $y = A \sin \left(B x - C\right) + D$.

#### Explanation:

$y = \frac{1}{2} \sin \left(x - \pi\right)$ can be looked at with $y = A \sin \left(B x - C\right) + D$

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

$\frac{2 \pi}{B} = p e r i o d$

$\frac{C}{B}$= phase shift

$D$=vertical shift

Amplitude = $\frac{1}{2}$

Period = $\frac{2 \pi}{1} = 2 \pi$

Phase shift = $\frac{\pi}{1} = \pi$ to the right

If the sign inside the parentheses is negative, the phase shift is right (or positive). If the sign inside the parentheses is positive, the phase shift is left (or negative).

The vertical shift in this problem is zero.