How do you find the amplitude, period, and phase shift of 3y=sin 2(x+1)?

Jun 1, 2018

As below.

Explanation:

Standard form of the sine function is

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

Given $3 y = \sin \left(2 x + 1\right)$

Writing it in standard form,

$y = \left(\frac{1}{3}\right) \sin \left(2 x + 2\right)$

$A m p l i t u \mathrm{de} = | A | = \left(\frac{1}{3}\right)$

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

Phase Shift $= - \frac{C}{B} = - \frac{2}{2} = - 1$, 1 to the left.

Vertical Shift $= D = 0$