Question

How do you graph `y=sin(1/2)(x+pi)`?

Answer 1

As below.

Explanation:

Standard form of sinusoidal function is `y = A sin (Bx - C) + D`

Given `y = sin ((1/2)(x + pi))`

`A = 1, B = (1/2), C = -pi, D = 0`

`Amplitude = |A| = 1`

Period `= (2pi)/|B| = (2pi) / (1/2) = 4 pi`

Phase Shift `= (-C) / B = (-(-pi/2)) / (1/2) = pi`, `color(red)(pi)` to the RIGHT

Vertical Shift `= D = 0`

graph{sin (x/2 + pi/2) [-10, 10, -5, 5]}