# How do you find the amplitude, period, and shift for #y = -5sin(x/2)#?

##### 2 Answers

**Amplitude**

**Period**

**Shift**

The **Vertical Shift (D) = 0**

#### Explanation:

Investigate the graph given below:

The **General Form** of the equation of the **Cos** function:

**A** represents the **Vertical Stretch Factor** and its **absolute value** is the **Amplitude.**

**B** is used to find the **Period (P)**:

**C**, if given, indicates that we have a **place shift** BUT **it is NOT equal** to

The **Place Shift** is actually equal to

**D** represents **Vertical Shift**.

We observe that

**Amplitude**

**Period**

**Shift**

The **Vertical Shift (D) = 0**

Hope this helps.

#### Explanation:

#"the standard form of the sine function is "#

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))#

#"where amplitude "=|a|," period "=(2pi)/b#

#"phase shift "=-c/b" and vertical shift "=d#

#"here "a=-5,b=1/2,c=d=0#

#"amplitude "=|-5|=5," period "=(2pi)/(1/2)=4pi#

#"there is no phase / vertical shift"#