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"