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

2 Answers
Dec 21, 2017

Amplitude #= |A| = |-5| = 5#

Period #" "=(2Pi)/(1/2) = 4Pi#

Shift #" "= C/B = 0/(1/2) = 0#

The Vertical Shift (D) = 0

Explanation:

Investigate the graph given below:

enter image source here

The General Form of the equation of the Cos function:

#color(green)(y = A*Sin(Bx + C) + D)#, where

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

B is used to find the Period (P):#" "P = (2Pi)/B#

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

The Place Shift is actually equal to #x# under certain special circumstances or conditions.

D represents Vertical Shift.

We observe that

Amplitude #= |A| = |-5| = 5#

Period #" "=(2Pi)/(1/2) = 4Pi#

Shift #" "= C/B = 0/(1/2) = 0#

The Vertical Shift (D) = 0

Hope this helps.

Dec 21, 2017

#5,4pi,0,0#

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"#