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

Oct 11, 2016

A = -1
$\tau = 2 \pi$
$\theta = - \frac{3 \pi}{4}$

#### Explanation:

The general form for a sine wave is:

$y = A \sin \left(B x + C\right) + D$

A is the amplitude
B is a number that contains the frequency, $f$, and the period, $\tau$

$B = 2 \pi f$
$f = \frac{B}{2 \pi}$

Because the $f = \frac{1}{\tau}$, the following is, also, true:

$B = \frac{2 \pi}{\tau}$
$\tau = \frac{2 \pi}{B}$

C is a number that contains the phase shift, $\theta$:

$\theta = \frac{C}{B}$

D is the vertical shift

Given:

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

The amplitude:

A = -1

The period:

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

The phase shift:

$\theta = - \frac{3 \pi}{4}$