# How do you graph y=sin x/2?

Oct 1, 2016

graph{y= sin(x/2) [-10, 10, -5, 5]}

#### Explanation:

Standard Form of a Sine Function: y=a sin (b(x-h))+k

a:
- Amplitude, half the distance from the highest to lowest point on the graph or the farthest distance from the mid line
- Vertical stretch (a>1) or vertical compression ( 1>a>0)
- Reflection across the x-axis (-a)

b:
- Period ( $\frac{2 \pi}{\left\mid b \right\mid}$) : The length of one cycle of the function
- Horizontal stretch (1>b>0) or horizontal compression (b>1)
- Reflection across the y-axis (-b)

h:
- Phase shift: If (x-h), the graph is shifted right, if (x+h), the graph is shifted left.

k:
- Mid line (y=k) : the horixantal line in the middle of the highest and lowest points on the graph
- Vertical shift by moving the mid line

y= sin (x/2)

Key Features:
Amplitude: 1
Period: 4$\pi$ ( $\frac{2 \pi}{\frac{1}{2}}$)
Phase shift: None
Midline: y=0