# What is the amplitude, period and the phase shift of #y = 2 sin (1/4 x)#?

##### 2 Answers

The amplitude is

#### Explanation:

We need

The period of a periodic function is

Here,

Therefore,

where the period is

So,

Then,

As

Therefore,

The amplitude is

The phase shift is

graph{2sin(1/4x) [-6.42, 44.9, -11.46, 14.2]}

#### 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)|)))#

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

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

#"here "a=2,b=1/4,c=d=0#

#"amplitude "=|2|=2," period "=(2pi)/(1/4)=8pi#

#"there is no phase shift"#